Searcharxiv⌕ Search

arXiv subjects

Bruce Williams

Publications and source records attributed to Bruce Williams.

10 recordsLinked to original sources
arXiv2021

Persephone: A Pluto-System Orbiter and Kuiper Belt Explorer

Persephone is a NASA concept mission study that addresses key questions raised by New Horizons' encounters with Kuiper Belt objects (KBOs), with arguably the most important being "Does Pluto have a subsurface ocean?". More broadly, Persephone would answer four significant science questions: (1) What are the internal structures of Pluto and Charon? (2) How have the surfaces and atmospheres in the Pluto system evolved? (3) How has the KBO population evolved? (4) What are the particles and magnetic field environments of the Kuiper Belt? To answer these questions, Persephone has a comprehensive payload, and would both orbit within the Pluto system and encounter other KBOs. The nominal mission is 30.7 years long, with launch in 2031 on a Space Launch System (SLS) Block 2 rocket with a Centaur kick stage, followed by a 27.6 year cruise powered by existing radioisotope electric propulsion (REP) and a Jupiter gravity assist to reach Pluto in 2058. En route to Pluto, Persephone would have one 50- to 100-km-class KBO encounter before starting a 3.1 Earth-year orbital campaign of the Pluto system. The mission also includes the potential for an 8-year extended mission, which would enable the exploration of another KBO in the 100- to 150-km-size class. The mission payload includes 11 instruments: Panchromatic and Color High-Resolution Imager; Low-Light Camera; Ultra-Violet Spectrometer; Near-Infrared (IR) Spectrometer; Thermal IR Camera; Radio Frequency Spectrometer; Mass Spectrometer; Altimeter; Sounding Radar; Magnetometer; and Plasma Spectrometer. The nominal cost of this mission is $3.0B, making it a large strategic science mission.

astro-ph.EP↗
arXiv2012

Homotopical Intersection Theory, III: multi-relative intersection problems

This paper extends some results of Hatcher and Quinn beyond the metastable range. We give a bordism theoretic obstruction to deforming a map between manifolds simultaneously off of a collection of pairwise disjoint submanifolds under the assumption that it can be deformed off of any proper subcollection in a homotopy coherent way. In a certain range of dimensions, ours is a complete obstruction to finding the desired deformation. We apply this machinery to embedding problems and to the study of linking phenomena.

math.AT↗
arXiv2012

Exotic smooth structures on topological fibre bundles I

When two smooth manifold bundles over the same base are fiberwise tangentially homeomorphic, the difference is measured by a homology class in the total space of the bundle. We call this the relative smooth structure class. Rationally and stably, this is a complete invariant. We give a more or less complete and self-contained exposition of this theory which is a reformulation of some of the results of [7]. An important application is the computation of the Igusa-Klein higher Reidemeister torsion invariants of these exotic smooth structures. Namely, the higher torsion invariant is equal to the Poincaré dual of the image of the smooth structure class in the homology of the base. This is proved in the companion paper [11] written by the first two authors.

math.KT↗
arXiv2010

Smoothing theory revisited

We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.

math.AT↗
arXiv2009

Equivalence of higher torsion invariants

We show that the smooth torsion of bundles of manifolds constructed by Dwyer, Weiss, and Williams satisfies the axioms for higher torsion developed by Igusa. As a consequence we obtain that the smooth Dwyer-Weiss-Williams torsion is proportional to the higher torsion of Igusa and Klein.

math.AT↗
arXiv2009

Homotopical Intersection Theory, II: equivariance

This is the second in a series of papers. Here we develop here an intersection theory for manifolds equipped with an action of a finite group. As in our previous paper, our approach will be homotopy theoretic, enabling us to circumvent the specter of equivariant transversality. This theory has applications to embedding problems, equivariant fixed point theory and the problem of enumerating the periodic points of a self map of a compact smooth manifold.

math.AT↗
arXiv2008

The refined transfer, bundle structures and algebraic K-theory

We give new homotopy theoretic criteria for deciding when a fibration with homotopy finite fibers admits a reduction to a fiber bundle with compact topological manifold fibers. The criteria lead to a new and unexpected result about homeomorphism groups of manifolds. A tool used in the proof is a surjective splitting of the assembly map for Waldhausen's functor A(X). We also give concrete examples of fibrations having a reduction to a fiber bundle with compact topological manifold fibers but which fail to admit a compact fiber smoothing. The examples are detected by algebraic K-theory invariants. We consider a refinement of the Becker-Gottlieb transfer. We show that a version of the axioms described by Becker and Schultz uniquely determines the refined transfer for the class of fibrations admitting a reduction to a fiber bundle with compact topological manifold fibers. In an appendix, we sketch a theory of characteristic classes for fibrations. The classes are primary obstructions to finding a compact fiber smoothing.

math.AT↗
arXiv2000

Automorphisms of manifolds

This is a survey paper on spaces of automorphisms of manifolds and spaces of manifolds in a fixed homotopy type. It describes the main theorems of traditional surgery theory, but also the main theorems of pseudoisotopy theory, alias concordance theory, Waldhausen style. It culminates in (an outline of) a synthesis of these two theories, producing algebraic models, valid in a stable range, for spaces of manifolds in a fixed homotopy type. This is inspired by earlier work of Burghelea-Lashof and Hatcher. The algebraic models are a mix of algebraic L-theory and algebraic K-theory.

math.AT↗
arXiv1998

Neighborhoods in Stratified Spaces with Two Strata

We develop a theory of tubular neighborhoods for the lower strata in manifold stratified spaces with two strata. In these topologically stratified spaces, manifold approximate fibrations and teardrops play the role that fibre bundles and mapping cylinders play in smoothly stratified spaces. Applications include the classification of neighborhood germs, the construction of exotic stratifications, a multiparameter isotopy extension theorem and an h-coborsism extension theorem.

math.GT↗