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Registered: 5/24/06

Ten papers published by Geometry & Topology Publications
Posted: Jul 11, 2012 7:57 AM

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Six papers have been published by Algebraic & Geometric Topology:

(1) Algebraic & Geometric Topology 12 (2012) 1313-1330
   Obstructions for constructing equivariant fibrations
     by Asli Guclukan Ilhan
   URL: http://www.msp.warwick.ac.uk/agt/2012/12-03/p050.xhtml
   DOI: 10.2140/agt.2012.12.1313

(2) Algebraic & Geometric Topology 12 (2012) 1331-1372
   Exponential growth of torsion in abelian coverings
     by Jean Raimbault
   URL: http://www.msp.warwick.ac.uk/agt/2012/12-03/p051.xhtml
   DOI: 10.2140/agt.2012.12.1331

(3) Algebraic & Geometric Topology 12 (2012) 1373-1403
   Modular isogeny complexes
     by Charles Rezk
   URL: http://www.msp.warwick.ac.uk/agt/2012/12-03/p052.xhtml
   DOI: 10.2140/agt.2012.12.1373

(4) Algebraic & Geometric Topology 12 (2012) 1405-1441
   Quadratic forms classify products on quotient ring spectra
     by Alain Jeanneret and Samuel Wuethrich
   URL: http://www.msp.warwick.ac.uk/agt/2012/12-03/p053.xhtml
   DOI: 10.2140/agt.2012.12.1405

(5) Algebraic & Geometric Topology 12 (2012) 1443-1455
   Cobordism of exact links
     by Vincent Blanloeil and Osamu Saeki
   URL: http://www.msp.warwick.ac.uk/agt/2012/12-03/p054.xhtml
   DOI: 10.2140/agt.2012.12.1443

(6) Algebraic & Geometric Topology 12 (2012) 1457-1486
   Spectral rigidity of automorphic orbits in free groups
     by Mathieu Carette, Stefano Francaviglia, Ilya Kapovich and
Armando Martino
   URL: http://www.msp.warwick.ac.uk/agt/2012/12-03/p055.xhtml
   DOI: 10.2140/agt.2012.12.1457

Four papers have been published by Geometry & Topology. Papers
(7) and (8) complete Issue 2 of Volume 16 and papers (9) and (10)
open Issue 3:

(7) Geometry & Topology 16 (2012) 1171-1203
   The Dirichlet Problem for constant mean curvature graphs in MxR
     by Abigail Folha and Harold Rosenberg
   URL: http://www.msp.warwick.ac.uk/gt/2012/16-02/p024.xhtml
   DOI: 10.2140/gt.2012.16.1171

(8) Geometry & Topology 16 (2012) 1205-1246
   Pattern rigidity and the Hilbert-Smith conjecture
     by Mahan Mj
   URL: http://www.msp.warwick.ac.uk/gt/2012/16-02/p025.xhtml
   DOI: 10.2140/gt.2012.16.1205

(9) Geometry & Topology 16 (2012) 1247-1320
   Deformation spaces of Kleinian surface groups are not locally
connected
     by Aaron D Magid
   URL: http://www.msp.warwick.ac.uk/gt/2012/16-03/p026.xhtml
   DOI: 10.2140/gt.2012.16.1247

(10) Geometry & Topology 16 (2012) 1321-1344
   On the nonexistence of certain branched covers
     by Pekka Pankka and Juan Souto
   URL: http://www.msp.warwick.ac.uk/gt/2012/16-03/p027.xhtml
   DOI: 10.2140/gt.2012.16.1321

Abstracts follow

(1) Obstructions for constructing equivariant fibrations
     by Asli Guclukan Ilhan

Let G be a finite group and calH be a family of subgroups of G which
is closed under conjugation and taking subgroups. Let B be a
G-CW--complex whose isotropy subgroups are in calH and let F= {F_H}_{H
in calH} be a compatible family of H-spaces. A G-fibration over B
with the fiber type calF = {F_H}_{H in calH} is a G-equivariant
fibration p: E -> B where p^-1(b) is G_b-homotopy equivalent to
F_{G_b} for each b in B. In this paper, we develop an obstruction
theory for constructing G-fibrations with the fiber type F over a
given G-CW--complex B. Constructing G-fibrations with a prescribed
fiber type F is an important step in the construction of free
G-actions on finite CW--complexes which are homotopy equivalent to a
product of spheres.

(2) Exponential growth of torsion in abelian coverings
     by Jean Raimbault

We show exponential growth of torsion numbers for links whose first
nonzero Alexander polynomial has positive logarithmic Mahler measure.
This extends a theorem of Silver and Williams to the case of a null
first Alexander polynomial and provides a partial solution for a
conjecture of theirs.

(3) Modular isogeny complexes
     by Charles Rezk

We describe a vanishing result on the cohomology of a cochain complex
associated to the moduli of chains of finite subgroup schemes on
elliptic curves. These results have applications to algebraic
topology, in particular to the study of power operations for Morava
E-theory at height 2.

(4) Quadratic forms classify products on quotient ring spectra
     by Alain Jeanneret and Samuel Wuethrich

We construct a free and transitive action of the group of bilinear
forms Bil(I/I^2[1]) on the set of R-products on F, a regular quotient
of an even E-infinity-ring spectrum R with F* isomorphic to R*/I. We
show that this action induces a free and transitive action of the
group of quadratic forms QF(I/I^2[1]) on the set of equivalence
classes of R-products on F. The characteristic bilinear form of F
introduced by the authors in a previous paper is the natural
obstruction to commutativity of F. We discuss the examples of the
Morava K-theories K(n) and the 2-periodic Morava K-theories K_n.

(5) Cobordism of exact links
     by Vincent Blanloeil and Osamu Saeki

A (2n-1)-dimensional (n-2)-connected closed oriented manifold smoothly
embedded in the sphere S^{2n+1} is called a (2n-1)-link. We introduce
the notion of exact links, which admit Seifert surfaces with good
homological conditions. We prove that for n >= 3, two exact
(2n-1)-links are cobordant if they have such Seifert surfaces with
algebraically cobordant Seifert forms. In particular, two fibered
(2n-1)-links are cobordant if and only if their Seifert forms with
respect to their fibers are algebraically cobordant. With this broad
class of exact links, we thus clarify the results of Blanloeil
[Ann. Fac. Sci. Toulouse Math. 7 (1998) 185-205] concerning cobordisms
of odd dimensional nonspherical links.

(6) Spectral rigidity of automorphic orbits in free groups
     by Mathieu Carette, Stefano Francaviglia, Ilya Kapovich and
Armando Martino

It is well-known that a point T in cv_N in the (unprojectivized)
Culler-Vogtmann Outer space cv_N is uniquely determined by its
translation length function ||.||_T: F_N --> R. A subset S of a free
group F_N is called spectrally rigid if, whenever T,T' in cv_N are
such that ||g||_T=||g||_T' for every g in S then T=T' in cv_N. By
contrast to the similar questions for the Teichmuller space, it is
known that for N >= 2 there does not exist a finite spectrally rigid
subset of F_N.

In this paper we prove that for N >= 3 if H <= Aut(F_N) is a subgroup
that projects to a nontrivial normal subgroup in Out(F_N) then the
H-orbit of an arbitrary nontrivial element g in F_N is spectrally
rigid. We also establish a similar statement for F_2=F(a,b), provided
that g in F_2 is not conjugate to a power of [a,b].

(7) The Dirichlet Problem for constant mean curvature graphs in MxR
     by Abigail Folha and Harold Rosenberg

We study graphs of constant mean curvature H>0 in M x R for M a
Hadamard surface, ie a complete simply connected surface with
curvature bounded above by a negative constant -a. We find necessary
and sufficient conditions for the existence of these graphs over
bounded domains in M, having prescribed boundary data, possibly
infinite.

(8) Pattern rigidity and the Hilbert-Smith conjecture
     by Mahan Mj

We initiate a study of the topological group PPQI(G,H) of
pattern-preserving quasi-isometries for G a hyperbolic Poincare
duality group and H an infinite quasiconvex subgroup of infinite index
in G. Suppose the boundary of G admits a visual metric d with
Hausdorff dimension less than the topological dimension plus 2.
Equivalently suppose that Ahlfors regular conformal dimension of the
boundary is less than the topological dimension plus 2.

(a) If Q_u is a group of pattern-preserving uniform quasi-isometries
(or more generally any locally compact group of pattern-preserving
quasi-isometries) containing G, then G is of finite index in Q_u.

(b) If instead, H is a codimension one filling subgroup, and Q is any
group of pattern-preserving quasi-isometries containing G, then G is
of finite index in Q. Moreover, if L is the limit set of H, calL is
the collection of translates of L under G, and Q is any
pattern-preserving group of homeomorphisms of the boundary of G
preserving calL and containing G, then the index of G in Q is finite
(Topological Pattern Rigidity).

We find analogous results in the realm of relative hyperbolicity,
regarding an equivariant collection of horoballs as a symmetric
pattern in the universal cover of a complete finite volume noncompact
manifold of pinched negative curvature. Our main result combined with
a theorem of Mosher, Sageev and Whyte gives QI rigidity results.

An important ingredient of the proof is a version of the
Hilbert--Smith conjecture for certain metric measure spaces, which
uses the full strength of Yang's theorem on actions of the p-adic
integers on homology manifolds. This might be of independent interest.

(9) Deformation spaces of Kleinian surface groups are not locally
connected
     by Aaron D Magid

For any closed surface S of genus g at least 2, we show that the
deformation space AH(S x I) of marked hyperbolic 3-manifolds homotopy
equivalent to S is not locally connected. This proves a conjecture of
Bromberg who recently proved that the space of Kleinian punctured
torus groups is not locally connected. Playing an essential role in
our proof is a new version of the filling theorem that is based on the
theory of cone-manifold deformations developed by Hodgson, Kerckhoff
and Bromberg.

(10) On the nonexistence of certain branched covers
     by Pekka Pankka and Juan Souto

We prove that while there are maps from T^4 to #^3(S^2 x S^2) of
arbitrarily large degree, there is no branched cover from the 4-torus
to #^3(S^2 x S^2). More generally, we obtain that, as long as a closed
manifold N satisfies a suitable cohomological condition, any
pi_1-surjective branched cover T^n to N is a homeomorphism.

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