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Geometry and Topology

Posts: 131
Registered: 5/24/06

Nine papers published by Geometry & Topology Publications
Posted: Feb 25, 2013 4:46 PM

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Six papers have been published by Algebraic & Geometric Topology

(1) Algebraic & Geometric Topology 13 (2013) 127-169
   The Arone-Goodwillie spectral sequence for Sigma^infty Omega^n
   and topological realization at odd primes
     by Sebastian Buescher, Fabian Hebestreit, Oliver Roendigs
     and Manfred Stelzer
   URL: http://www.msp.warwick.ac.uk/agt/2013/13-01/p005.xhtml
   DOI: 10.2140/agt.2013.13.127

(2) Algebraic & Geometric Topology 13 (2013) 171-203
   Transchromatic generalized character maps
     by Nathaniel Stapleton
   URL: http://www.msp.warwick.ac.uk/agt/2013/13-01/p006.xhtml
   DOI: 10.2140/agt.2013.13.171

(3) Algebraic & Geometric Topology 13 (2013) 205-235
   Explicit angle structures for veering triangulations
     by David Futer and Francois Gueritaud
   URL: http://www.msp.warwick.ac.uk/agt/2013/13-01/p007.xhtml
   DOI: 10.2140/agt.2013.13.205

(4) Algebraic & Geometric Topology 13 (2013) 237-275
   Cascades and perturbed Morse-Bott functions
     by Augustin Banyaga and David E Hurtubise
   URL: http://www.msp.warwick.ac.uk/agt/2013/13-01/p008.xhtml
   DOI: 10.2140/agt.2013.13.237

(5) Algebraic & Geometric Topology 13 (2013) 277-312
   Dirac operators and symmetries of quasitoric manifolds
     by Michael Wiemeler
   URL: http://www.msp.warwick.ac.uk/agt/2013/13-01/p009.xhtml
   DOI: 10.2140/agt.2013.13.277

(6) Algebraic & Geometric Topology 13 (2013) 313-374
   Derivators, pointed derivators and stable derivators
     by Moritz Groth
   URL: http://www.msp.warwick.ac.uk/agt/2013/13-01/p010.xhtml
   DOI: 10.2140/agt.2013.13.313

Three papers have been published by Geometry & Topology

(7) Geometry & Topology 17 (2013) 39-71
   Noncoherence of arithmetic hyperbolic lattices
     by Michael Kapovich
   URL: http://www.msp.warwick.ac.uk/gt/2013/17-01/p002.xhtml
   DOI: 10.2140/gt.2013.17.39

(8) Geometry & Topology 17 (2013) 73-92
   Deriving Deligne-Mumford stacks with perfect obstruction theories
     by Timo Schuerg
   URL: http://www.msp.warwick.ac.uk/gt/2013/17-01/p003.xhtml
   DOI: 10.2140/gt.2013.17.73

(9) Geometry & Topology 17 (2013) 93-156
   Width is not additive
     by Ryan Blair and Maggy Tomova
   URL: http://www.msp.warwick.ac.uk/gt/2013/17-01/p004.xhtml
   DOI: 10.2140/gt.2013.17.93

Abstracts follow

(1) The Arone-Goodwillie spectral sequence for Sigma^infty Omega^n
   and topological realization at odd primes
     by Sebastian Buescher, Fabian Hebestreit, Oliver Roendigs
     and Manfred Stelzer

We employ the Goodwillie spectral sequence for the iterated loop space
functor in order to provide realizability conditions on certain
unstable modules over the Steenrod algebra at an odd prime.

(2) Transchromatic generalized character maps
     by Nathaniel Stapleton

The generalized character map of Hopkins, Kuhn, and Ravenel
[J. Amer. Math. Soc. 13 (2000) 553-594] can be interpreted as a map of
cohomology theories beginning with a height n cohomology theory E and
landing in a height 0 cohomology theory with a rational algebra of
coefficients that is constructed out of E. We use the language of
p-divisible groups to construct extensions of the generalized
character map for Morava E-theory to every height between 0 and n.

(3) Explicit angle structures for veering triangulations
     by David Futer and François Guéritaud

Agol recently introduced the notion of a veering triangulation, and
showed that such triangulations naturally arise as layered
triangulations of fibered hyperbolic 3-manifolds. We prove, by a
constructive argument, that every veering triangulation admits
positive angle structures, recovering a result of Hodgson, Rubinstein,
Segerman, and Tillmann. Our construction leads to explicit lower
bounds on the smallest angle in this positive angle structure, and to
information about angled holonomy of the boundary tori.

(4) Cascades and perturbed Morse-Bott functions
     by Augustin Banyaga and David E Hurtubise

Let f:M -> R be a Morse-Bott function on a finite-dimensional closed
smooth manifold M. Choosing an appropriate Riemannian metric on M and
Morse-Smale functions f_j:C_j -> R on the critical submanifolds C_j,
one can construct a Morse chain complex whose boundary operator is
defined by counting cascades [Int. Math. Res. Not. 42 (2004)
2179-2269]. Similar data, which also includes a parameter e > 0
that scales the Morse-Smale functions f_j, can be used to define an
explicit perturbation of the Morse-Bott function f to a Morse-Smale
function h_e:M -> R [Progr. Math. 133 (1995) 123-183; Ergodic Theory
Dynam. Systems 29 (2009) 1693-1703]. In this paper we show that the
Morse-Smale-Witten chain complex of h_e is the same as the Morse chain
complex defined using cascades for any e > 0 sufficiently small. That
is, the two chain complexes have the same generators, and their
boundary operators are the same (up to a choice of sign). Thus, the
Morse Homology Theorem implies that the homology of the cascade chain
complex of f:M -> R is isomorphic to the singular homology H_*(M; Z).

(5) Dirac operators and symmetries of quasitoric manifolds
     by Michael Wiemeler

We establish a vanishing result for indices of certain twisted Dirac
operators on Spin^c-manifolds with nonabelian Lie group actions. We
apply this result to study nonabelian symmetries of quasitoric
manifolds. We give upper bounds for the degree of symmetry of these
manifolds.

(6) Derivators, pointed derivators and stable derivators
     by Moritz Groth

We develop some aspects of the theory of derivators, pointed
derivators and stable derivators. Stable derivators are shown to
canonically take values in triangulated categories. Similarly, the
functors belonging to a stable derivator are canonically exact so that
stable derivators are an enhancement of triangulated categories. We
also establish a similar result for additive derivators in the context
of pretriangulated categories. Along the way, we simplify the notion
of a pointed derivator, reformulate the base change axiom and give a
new proof that a combinatorial model category has an underlying
derivator.

(7) Noncoherence of arithmetic hyperbolic lattices
     by Michael Kapovich

We prove that all arithmetic lattices in O(n,1), n>= 4, n not 7, are
noncoherent. We also establish noncoherence of uniform arithmetic
lattices of the simplest type in SU(n,1), n>= 2, and of uniform
lattices in SU(2,1) which have infinite abelianization.

(8) Deriving Deligne-Mumford stacks with perfect obstruction theories
     by Timo Schürg

We show that every n-connective quasi-coherent obstruction theory on a
Deligne-Mumford stack comes from the structure of a connective
spectral Deligne-Mumford stack on the underlying topos. Working over a
base ring containing the rationals, we obtain the corresponding result
for derived Deligne-Mumford stacks.

(9) Width is not additive
     by Ryan Blair and Maggy Tomova

We develop the construction suggested by Scharlemann and Thompson in
[Proc. of the Casson Fest. (2004) 135-144] to obtain an infinite
family of pairs of knots K_a and K'_a so that w(K_a # K'_a) = max
{w(K_a), w(K'_a)}. This is the first known example of a pair of knots
such that w(K # K') < w(K) + w(K') - 2 and it establishes that the
lower bound w(K # K') >= max {w(K), w(K')} obtained in Scharlemann
and Schultens [Trans. Amer. Math. Soc. 358 (2006) 3781-3805] is best
possible. Furthermore, the knots K_a provide an example of knots
where the number of critical points for the knot in thin position is
greater than the number of critical points for the knot in bridge
position.

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