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T. Porter

Publications and source records attributed to T. Porter.

7 recordsLinked to original sources

SKA studies of in-situ synchrotron radiation from molecular clouds

Observations of the properties of dense molecular clouds are critical in understanding the process of star-formation. One of the most important, but least understood, is the role of the magnetic fields. We discuss the possibility of using high-resolution, high-sensitivity radio observations with the SKA to measure for the first time the in-situ synchrotron radiation from these molecular clouds. If the cosmic-ray (CR) particles penetrate clouds as expected, then we can measure the B-field strength directly using radio data. So far, this signature has never been detected from the collapsing clouds themselves and would be a unique probe of the magnetic field. Dense cores are typically ~0.05 pc in size, corresponding to ~arcsec at ~kpc distances, and flux density estimates are ~mJy at 1 GHz. The SKA should be able to readily detect directly, for the first time, along lines-of-sight that are not contaminated by thermal emission or complex foreground/background synchrotron emission. Polarised synchrotron may also be detectable providing additional information about the regular/turbulent fields.

astro-ph.GA

Global actions, groupoid atlases and related topics

A. Bak developed a combinatorial approach to higher $K$-theory, in which control is kept of the elementary operations involved, through paths and `paths of paths' in what he called a global action. The homotopy theory of these was developed by G. Minian. R. Brown and T. Porter developed applications to identities among relations for groups, and also the extension to groupoid atlases. This paper is intended as an introduction tothis circle of ideas, and so to give a basis for exploration and development of this area.

math.AT

A homotopy double groupoid of a Hausdorff space II: a van Kampen theorem

This paper is the second in a series exploring the properties of a functor which assigns a homotopy double groupoid with connections to a Hausdorff space. We show that this functor satisfies a version of the van Kampen theorem, and so is a suitable tool for nonabelian, 2-dimensional, local-to-global problems. The methods are analogous to those developed by Brown and Higgins for similar theorems for other higher homotopy groupoids. An integral part of the proof is a detailed discussion of commutative cubes in a double category with connections, and a proof of the key result that any composition of commutative cubes is commutative. These results have recently been generalised to all dimensions by Philip Higgins.

math.AT

Crossed squares and 2-crossed modules

Crossed squares and 2-crossed modules are both algebraic models for 3-types. This paper explores the interrelationships between these two models.

math.KT

Joins for (Augmented) Simplicial Sets

We introduce a notion of join for (augmented) simplicial sets generalising the classical join of geometric simplicial complexes. The definition comes naturally from the ordinal sum on the base simplicial category $Δ$.

math.CT

Freeness conditions for crossed squares and squared complexes

Following Ellis, we investigate the notion of totally free crossed squares and related square complexes. It is shown how to interpret the information in a free simplicial group given with a choice of CW-basis, in terms of the data for a totally free crossed square. Results of Ellis then apply to give a description in terms of tensor products of crossed modules. The paper ends with a purely algebraic derivation of a result of Brown and Loday.

math.KT