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Michael W. Davis

Publications and source records attributed to Michael W. Davis.

18 recordsLinked to original sources
arXiv2026

The Ultraviolet Spectrograph on ESA's Jupiter Icy Moons Explorer Mission (JUICE-UVS)

The Jupiter Icy Moons Explorer (JUICE) mission, led by ESA, has an Ultraviolet Spectrograph (JUICE-UVS) contributed by NASA and built at Southwest Research Institute. JUICE-UVS is designed to provide a diversity of measurements to further our understanding of the potential habitability of icy ocean worlds at Jupiter and to study Jupiter and the Jovian system as an archetype for gas giants. JUICE-UVS observes photons in the 50-204 nm wavelength range at moderate spectral and spatial resolution along a 7.5 deg slit composed of 7.3 deg x 0.1 deg and 0.2 deg x 0.2 deg contiguous sections. JUICE-UVS performs a comprehensive study of icy satellite atmospheres, plumes, surfaces, and local space environments; Jupiter's atmosphere and aurora; Io and its Io Plasma Torus; and other Jupiter system targets (rings, small moons, etc.) as available. The variety of observational techniques employed include: nadir push-broom imaging, disk scans, limb stares, stellar and solar occultations, Jupiter transit observations, and neutral cloud/plasma torus stares and scans. This paper describes the UVS investigation's science plans, instrument details, concept of operations, and data formats in the context of the JUICE mission's habitability and Jupiter system goals.

astro-ph.EP↗
arXiv2021

Illuminating Galaxy Evolution at Cosmic Noon with ISCEA: the Infrared Satellite for Cosmic Evolution Astrophysics

ISCEA (Infrared Satellite for Cosmic Evolution Astrophysics) is a small astrophysics mission whose Science Goal is to discover how galaxies evolved in the cosmic web of dark matter at cosmic noon. Its Science Objective is to determine the history of star formation and its quenching in galaxies as a function of local density and stellar mass when the Universe was 3-5 Gyrs old (1.2 10 Mpc in each of 50 protocluster (cluster and cosmic web) fields at 1.2 < z < 2.1. ISCEA measures the star formation quenching factor in those fields, and galaxy kinematics with a precision < 50 km/s to deduce the 3D spatial distribution in each field. ISCEA will transform our understanding of galaxy evolution at cosmic noon. ISCEA is a small satellite observatory with a 30cm equivalent diameter aperture telescope with a FoV of 0.32 deg^2, and a multi-object spectrograph with a digital micro-mirror device (DMD) as its programmable slit mask. ISCEA will obtain spectra of 1000 galaxies simultaneously at an effective resolving power of R=1000, with 2.8"x2.8" slits, over the NIR wavelength range of 1.1 to 2.0 microns, a regime not accessible from the ground without large gaps in coverage. ISCEA will achieve a pointing accuracy of <= 2" FWHM over 200s. ISCEA will be launched into a Low Earth Orbit, with a prime mission of 2.5 years. ISCEA's space-qualification of DMDs opens a new window for spectroscopy from space, enabling revolutionary advances in astrophysics.

astro-ph.GA↗
arXiv2020

Bordifications of hyperplane arrangements and their curve complexes

The complement of an arrangement of hyperplanes in $\mathbb C^n$ has a natural bordification to a manifold with corners formed by removing (or "blowing up") tubular neighborhoods of the hyperplanes and certain of their intersections. When the arrangement is the complexification of a real simplicial arrangement, the bordification closely resembles Harvey's bordification of moduli space. We prove that the faces of the universal cover of the bordification are parameterized by the simplices of a simplicial complex $\mathcal{C}$, the vertices of which are the irreducible "parabolic subgroups" of the fundamental group of the arrangement complement. So, the complex $\mathcal{C}$ plays a similar role for an arrangement complement as the curve complex does for moduli space. Also, in analogy with curve complexes and with spherical buildings, we prove that $\mathcal{C}$ has the homotopy type of a wedge of spheres.

math.GT↗
arXiv2018

The Lyman-α Sky Background as Observed by New Horizons

Recent observations of interplanetary medium (IPM) atomic hydrogen Lyman-α (Lyα) emission in the outer solar system, made with the Alice ultraviolet spectrograph on New Horizons (NH), are presented. The observations include regularly spaced great-circle scans of the sky and pointed observations near the downstream and upstream flow directions of interstellar H atoms. The NH Alice data agree very well with the much earlier Voyager UVS results, after these are reduced by a factor of 2.4 in brightness, in accordance with recent re-analyses. In particular, the falloff of IPM Lyα brightness in the upstream-looking direction as a function of spacecraft distance from the Sun is well-matched by an expected 1/r dependence, but with an added constant brightness of ~40 Rayleighs. This additional brightness is a possible signature of the hydrogen wall at the heliopause or of a more distant background. Ongoing observations are planned at a cadence of roughly twice per year.

astro-ph.EP↗
arXiv2018

Action dimensions of some simple complexes of groups

The action dimension of a discrete group $G$ is the minimum dimension of contractible manifold that admits a proper $G$-action. We compute the action dimension of the direct limit of a simple complex of groups for several classes of examples including: 1) Artin groups, 2) graph products of groups, and 3) fundamental groups of aspherical complements of arrangements of affine hyperplanes.

math.GT↗
arXiv2016

Determining the action dimension of an Artin group by using its complex of abelian subgroups

Suppose that $(W,S)$ is a Coxeter system with associated Artin group $A$ and with a simplicial complex $L$ as its nerve. We define the notion of a "standard abelian subgroup" in $A$. The poset of such subgroups in $A$ is parameterized by the poset of simplices in a certain subdivision $L_\oslash$ of $L$. This complex of standard abelian subgroups is used to generalize an earlier result from the case of right-angled Artin groups to case of general Artin groups, by calculating, in many instances, the smallest dimension of a manifold model for $BA$. (This is the "action dimension" of $A$ denoted actdim $A$.) If $H_d(L; \mathbb Z/2)\neq 0$, where $d=\dim L$, then actdim $A \ge 2d+2$. Moreover, when the $K(π,1)$-Conjecture holds for $A$, the inequality is an equality.

math.GT↗
arXiv2016

Complements of hyperplane arrangements as posets of spaces

The complement of an arrangement A of a finite number of affine hyperplanes in complex n-space has the structure of a poset of spaces indexed by the intersection poset, L(A). The space corresponding to G in L(A) is homotopy equivalent to the complement of the hyperplanes in the central arrangement A_G normal to G. This poset of spaces structure can be used to repair a spectral sequence argument in two earlier papers of Davis, Januszkiewicz, Leary and Okun for computing certain cohomology groups of arrangement complements. Similarly, toric hyperplane arrangements have the structure of a diagram of spaces and this structure can be used fix a spectral sequence argument in an earlier paper of Davis and Settepanella.

math.AT↗
arXiv2015

Right-angularity, flag complexes, asphericity. \ Criteria for asphericity: corrigenda for "Right-angularity, flag complexes, asphericity"

The "polyhedral product functor" produces a space from a simplicial complex L and a collection of pairs of spaces, {(A(i),B(i))}, where i ranges over the vertex set of L. We give necessary and sufficient conditions for the resulting space to be aspherical. There are two similar constructions, each of which starts with a space X and a collection of subspaces, {X_i} and then produces a new space. We give conditions for the results of these constructions to be aspherical. All three techniques can be used to produce examples of closed aspherical manifolds. Abstract for Corrigenda: This note concerns two refinements to the earlier work by the first author. First, when L is infinite, the definition of polyhedral product needs clarification. Second, the earlier paper omitted some subtle parts of the necessary and sufficient conditions for polyhedral products to be aspherical. Correct versions of these necessary and sufficient conditions are given in the present paper.

math.GT↗
arXiv2014

The action dimension of right-angled Artin groups

The action dimension of a discrete group $Γ$ is the smallest dimension of a contractible manifold which admits a proper action of $Γ$. Associated to any flag complex $L$ there is a right-angled Artin group, $A_L$. We compute the action dimension of $A_L$ for many $L$. Our calculations come close to confirming the conjecture that if an $\ell^2$-Betti number of $A_L$ in degree $l$ is nonzero, then the action dimension of $A_L$ is $\ge 2l$.

math.GT↗
arXiv2014

Euler characteristics of generalized Haken manifolds

Haken n-manifolds have been defined and studied by B. Foozwell and H. Rubinstein in analogy with the classical Haken manifolds of dimension 3, based upon the the theory of boundary patterns developed by K. Johannson. The Euler characteristic of a Haken manifold is analyzed and shown to be equal to the sum of the Charney-Davis invariants of the duals of the boundary complexes of the n-cells at the end of a hierarchy. These dual complexes are shown to be flag complexes. It follows that the Charney-Davis Conjecture is equivalent to the Euler Characteristic Sign Conjecture for Haken manifolds. Since the Charney-Davis invariant of a flag simplicial 3-sphere is known to be non-negative it follows that a closed Haken 4-manifold has non-negative Euler characteristic. These results hold as well for generalized Haken manifolds whose hierarchies can end with compact contractible manifolds rather than cells.

math.GT↗
arXiv2013

Random graph products of finite groups are rational duality groups

Given an edge-independent random graph G(n,p), we determine various facts about the cohomology of graph products of groups for the graph G(n,p). In particular, the random graph product of a sequence of finite groups is a rational duality group with probability tending to 1 as n goes to infinity. This includes random right angled Coxeter groups as a special case.

math.GR↗
arXiv2013

When are two Coxeter orbifolds diffeomorphic?

One can define what it means for a compact manifold with corners to be a "contractible manifold with contractible faces." Two combinatorially equivalent, contractible manifolds with contractible faces are diffeomorphic if and only if their 4-dimensional faces are diffeomorphic. It follows that two simple convex polytopes are combinatorially equivalent if and only if they are diffeomorphic as manifolds with corners. On the other hand, by a result of Akbulut, for each n > 3, there are smooth, contractible n-manifolds with contractible faces which are combinatorially equivalent but not diffeomorphic. Applications are given to rigidity questions for reflection groups and smooth torus actions.

math.GT↗
arXiv2013

Aspherical manifolds that cannot be triangulated

Although Kirby and Siebenmann showed that there are manifolds that do not admit PL structures, the possibility remained that all manifolds could be triangulated. In the late seventies Galewski and Stern and independently Matumoto showed that non-triangulable manifolds exist in all dimensions > 4 if and only if homology 3-spheres with certain properties do not exist. In 2013 Manolescu showed that, indeed, there were no such homology 3-spheres and hence, non-triangulable manifolds exist in each dimension >4. It follows from work of Freedman in 1982 that there are 4-manifolds that cannot be triangulated. In 1991 Davis and Januszkiewicz applied a hyperbolization procedure to Freedman's 4-manifolds to get closed aspherical 4-manifolds that cannot be triangulated. In this paper we apply hyperbolization techniques to the Galewski-Stern manifolds to show that there exist closed aspherical n-manifolds that cannot be triangulated for each n> 5. The question remains open in dimension 5.

math.GT↗
arXiv2012

Temporal Variability of Lunar Exospheric Helium During January 2012 from LRO/LAMP

We report observations of the lunar helium exosphere made between December 29, 2011, and January 26, 2012, with the Lyman Alpha Mapping Project (LAMP) ultraviolet spectrograph on NASA's Lunar Reconnaissance Orbiter Mission (LRO). The observations were made of resonantly scattered He I 584 from illuminated atmosphere against the dark lunar surface on the dawn side of the terminator. We find no or little variation of the derived surface He density with latitude but day-to-day variations that likely reflect variations in the solar wind alpha flux. The 5-day passage of the Moon through the Earth's magnetotail results in a factor of two decrease in surface density, which is well explained by model simulations.

astro-ph.EP↗
arXiv2011

The Euler characteristic of a polyhedral product

Given a finite simplicial complex L and a collection of pairs of spaces indexed by its vertex set, one can define their polyhedral product. We record a simple formula for its Euler characteristic. In special cases the formula simplifies further to one involving the h-polynomial of L.

math.GT↗
arXiv2010

Cohomology computations for Artin groups, Bestvina-Brady groups, and graph products

We compute: * the cohomology with group ring coefficients of Artin groups (or actually, of their associated Salvetti complexes), Bestvina-Brady groups, and graph products of groups, * the L^2-Betti numbers of Bestvina-Brady groups and of graph products of groups, * the weighted L^2-Betti numbers of graph products of Coxeter groups. In the case of arbitrary graph products there is an additional proviso: either all factors are infinite or all are finite.(However, for graph products of Coxeter groups this proviso is unnecessary.)

math.GR↗
arXiv1999

Piecewise Euclidean structures and Eberlein's Rigidity Theorem in the singular case

In this article, we generalize Eberlein's Rigidity Theorem to the singular case, namely, one of the spaces is only assumed to be a CAT(0) topological manifold. As a corollary, we get that any compact irreducible but locally reducible locally symmetric space of noncompact type does not admit a nonpositively curved (in the Aleksandrov sense) piecewise Euclidean structure. Any hyperbolic manifold, on the other hand, does admit such a structure.

math.GT↗