Eight papers published by Geometry & Topology Publications

[Geometry and Topology]

Papers (1) to (4) open Volume 13 (2013) of Algebraic & Geometric Topology

(1) Algebraic & Geometric Topology 13 (2013) 1-34
Topological K-(co)homology of classifying spaces of discrete groups
by Michael Joachim and Wolfgang Lueck
URL: http://www.msp.warwick.ac.uk/agt/2013/13-01/p001.xhtml
DOI: 10.2140/agt.2013.13.1

(2) Algebraic & Geometric Topology 13 (2013) 35-60
Spherical alterations of handles: embedding the manifold plus construction
by Craig R Guilbault and Frederick C Tinsley
URL: http://www.msp.warwick.ac.uk/agt/2013/13-01/p002.xhtml
DOI: 10.2140/agt.2013.13.35

(3) Algebraic & Geometric Topology 13 (2013) 61-114
Complete intersections and mod p cochains
by David J Benson, John P C Greenlees and Shoham Shamir
URL: http://www.msp.warwick.ac.uk/agt/2013/13-01/p003.xhtml
DOI: 10.2140/agt.2013.13.61

(4) Algebraic & Geometric Topology 13 (2013) 115-125
Conservative subgroup separability for surfaces with boundary
by Mark D Baker and Daryl Cooper
URL: http://www.msp.warwick.ac.uk/agt/2013/13-01/p004.xhtml
DOI: 10.2140/agt.2013.13.115

Papers (5), (6) and (7) complete Volume 16 (2012) of Geometry &
Topology whilst paper (8) opens Volume 17 (2013)

(5) Geometry & Topology 16 (2012) 2391-2426
A splitting theorem for nonnegatively curved Alexandrov spaces
by Andreas Woerner
URL: http://www.msp.warwick.ac.uk/gt/2012/16-04/p051.xhtml
DOI: 10.2140/gt.2012.16.2391

(6) Geometry & Topology 16 (2012) 2427-2479
Nonvarying sums of Lyapunov exponents of Abelian differentials in low genus
by Dawei Chen and Martin Moeller
URL: http://www.msp.warwick.ac.uk/gt/2012/16-04/p052.xhtml
DOI: 10.2140/gt.2012.16.2427

(7) Geometry & Topology 16 (2012) 2481-2516
The Ingram conjecture
by Marcy Barge, Henk Bruin and Sonja Stimac
URL: http://www.msp.warwick.ac.uk/gt/2012/16-04/p053.xhtml
DOI: 10.2140/gt.2012.16.2481

(8) Geometry & Topology 17 (2013) 1-37
Asymptotics of classical spin networks
by Stavros Garoufalidis and Roland van der Veen
Appendix: Don Zagier
URL: http://www.msp.warwick.ac.uk/gt/2013/17-01/p001.xhtml
DOI: 10.2140/gt.2013.17.1

Abstracts follow

(1) Topological K-(co)homology of classifying spaces of discrete groups
by Michael Joachim and Wolfgang Lueck

Let G be a discrete group. We give methods to compute, for a
generalized (co)homology theory, its values on the Borel construction
EG cross_G X of a proper G-CW-complex X satisfying certain finiteness
conditions. In particular we give formulas computing the topological
K-(co)homology K_*(BG) and K^*(BG) up to finite abelian torsion
groups. They apply for instance to arithmetic groups, word hyperbolic
groups, mapping class groups and discrete cocompact subgroups of
almost connected Lie groups. For finite groups G these formulas are
sharp. The main new tools we use for the K-theory calculation are
a Cocompletion Theorem and Equivariant Universal Coefficient Theorems
which are of independent interest. In the case where $G$ is a finite
group these theorems reduce to well-known results of Greenlees and
Boekstedt.



(2) Spherical alterations of handles: embedding the manifold plus construction
by Craig R Guilbault and Frederick C Tinsley

Quillen's famous plus construction plays an important role in many
aspects of manifold topology. In our own work [Geometry and Topology 7
(2006) 541-556] on ends of open manifolds, an ability to embed
cobordisms provided by the plus construction into the manifolds being
studied was a key to completing the main structure theorem. In this
paper we develop a ``spherical modification'' trick that allows for a
constructive approach to obtaining those embeddings. More importantly,
this approach can be used to obtain more general embedding results. In
this paper we develop generalizations of the plus construction
(together with the corresponding group-theoretic notions) and show how
those cobordisms can be embedded in manifolds satisfying appropriate
fundamental group properties. Results obtained here are motivated by,
and play an important role in, our ongoing study of noncompact
manifolds.


(3) Complete intersections and mod p cochains
by David J Benson, John P C Greenlees and Shoham Shamir

We give homotopy invariant definitions corresponding to three
well-known properties of complete intersections, for the ring, the
module theory and the endomorphisms of the residue field, and we
investigate them for the mod p cochains on a space, showing that
suitable versions of the second and third are equivalent and that the
first is stronger. We are particularly interested in classifying
spaces of groups, and we give a number of examples. The case of
rational homotopy theory is treated in [J. Pure Appl. Algebra 217
(2013) 636--663], and there are some interesting contrasts.


(4) Conservative subgroup separability for surfaces with boundary
by Mark D Baker and Daryl Cooper

If F is a compact surface with boundary, then a finitely generated
subgroup without peripheral elements of G = pi_1(F) can be separated
from finitely many other elements of G by a finite index subgroup of G
corresponding to a finite cover F' with the same number of boundary
components as F.


(5) A splitting theorem for nonnegatively curved Alexandrov spaces
by Andreas Woerner

We study Alexandrov spaces of nonnegative curvature whose boundaries
consist of several strata of codimension 1. If the space is compact and
the common intersection of all boundary strata is empty, then the space
is a metric product. In particular, this is fulfilled if the compact
space has dimension n and contains more than n+1 boundary strata. The
splitting factors are in general non-flat.


(6) Nonvarying sums of Lyapunov exponents of Abelian differentials in low genus
by Dawei Chen and Martin Moeller
We show that for many strata of Abelian differentials in
low genus the sum of Lyapunov exponents for the Teichmueller geodesic
flow is the same for all Teichmueller curves in that stratum, hence
equal to the sum of Lyapunov exponents for the whole stratum. This
behavior is due to the disjointness property of Teichmueller curves
with various geometrically defined divisors on moduli spaces of
curves.


(7) The Ingram conjecture
by Marcy Barge, Henk Bruin and Sonja Stimac

We prove the Ingram conjecture, ie we show that the inverse limit
spaces of every two tent maps with different slopes in the interval
[1,2] are nonhomeomorphic. Based on the structure obtained from the
proof, we also show that every self-homeomorphism of the inverse limit
space of the tent map is pseudo-isotopic, on the core, to some power
of the shift homeomorphism.


(8) Asymptotics of classical spin networks
by Stavros Garoufalidis and Roland van der Veen
Appendix: Don Zagier

A spin network is a cubic ribbon graph labeled by representations of
SU(2). Spin networks are important in various areas of Mathematics
(3-dimensional Quantum Topology), Physics (Angular Momentum, Classical
and Quantum Gravity) and Chemistry (Atomic Spectroscopy). The
evaluation of a spin network is an integer number. The main results
of our paper are:
(a) an existence theorem for the asymptotics of evaluations of
arbitrary spin networks (using the theory of G-functions),
(b) a rationality property of the generating series of all evaluations
with a fixed underlying graph (using the combinatorics of the
chromatic evaluation of a spin network),
(c) rigorous effective computations of our results for some 6j-symbols
using the Wilf-Zeilberger theory, and
(d) a complete analysis of the regular Cube 12j spin network
(including a nonrigorous guess of its Stokes constants), in the
appendix.



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