Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.



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


Six papers have been published by Algebraic & Geometric Topology:
(1) Algebraic & Geometric Topology 12 (2012) 13131330 Obstructions for constructing equivariant fibrations by Asli Guclukan Ilhan URL: http://www.msp.warwick.ac.uk/agt/2012/1203/p050.xhtml DOI: 10.2140/agt.2012.12.1313
(2) Algebraic & Geometric Topology 12 (2012) 13311372 Exponential growth of torsion in abelian coverings by Jean Raimbault URL: http://www.msp.warwick.ac.uk/agt/2012/1203/p051.xhtml DOI: 10.2140/agt.2012.12.1331
(3) Algebraic & Geometric Topology 12 (2012) 13731403 Modular isogeny complexes by Charles Rezk URL: http://www.msp.warwick.ac.uk/agt/2012/1203/p052.xhtml DOI: 10.2140/agt.2012.12.1373
(4) Algebraic & Geometric Topology 12 (2012) 14051441 Quadratic forms classify products on quotient ring spectra by Alain Jeanneret and Samuel Wuethrich URL: http://www.msp.warwick.ac.uk/agt/2012/1203/p053.xhtml DOI: 10.2140/agt.2012.12.1405
(5) Algebraic & Geometric Topology 12 (2012) 14431455 Cobordism of exact links by Vincent Blanloeil and Osamu Saeki URL: http://www.msp.warwick.ac.uk/agt/2012/1203/p054.xhtml DOI: 10.2140/agt.2012.12.1443
(6) Algebraic & Geometric Topology 12 (2012) 14571486 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/2012/1203/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) 11711203 The Dirichlet Problem for constant mean curvature graphs in MxR by Abigail Folha and Harold Rosenberg URL: http://www.msp.warwick.ac.uk/gt/2012/1602/p024.xhtml DOI: 10.2140/gt.2012.16.1171
(8) Geometry & Topology 16 (2012) 12051246 Pattern rigidity and the HilbertSmith conjecture by Mahan Mj URL: http://www.msp.warwick.ac.uk/gt/2012/1602/p025.xhtml DOI: 10.2140/gt.2012.16.1205
(9) Geometry & Topology 16 (2012) 12471320 Deformation spaces of Kleinian surface groups are not locally connected by Aaron D Magid URL: http://www.msp.warwick.ac.uk/gt/2012/1603/p026.xhtml DOI: 10.2140/gt.2012.16.1247
(10) Geometry & Topology 16 (2012) 13211344 On the nonexistence of certain branched covers by Pekka Pankka and Juan Souto URL: http://www.msp.warwick.ac.uk/gt/2012/1603/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 GCWcomplex whose isotropy subgroups are in calH and let F= {F_H}_{H in calH} be a compatible family of Hspaces. A Gfibration over B with the fiber type calF = {F_H}_{H in calH} is a Gequivariant fibration p: E > B where p^1(b) is G_bhomotopy equivalent to F_{G_b} for each b in B. In this paper, we develop an obstruction theory for constructing Gfibrations with the fiber type F over a given GCWcomplex B. Constructing Gfibrations with a prescribed fiber type F is an important step in the construction of free Gactions on finite CWcomplexes 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 Etheory 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 Rproducts on F, a regular quotient of an even Einfinityring 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 Rproducts 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 Ktheories K(n) and the 2periodic Morava Ktheories K_n.
(5) Cobordism of exact links by Vincent Blanloeil and Osamu Saeki
A (2n1)dimensional (n2)connected closed oriented manifold smoothly embedded in the sphere S^{2n+1} is called a (2n1)link. We introduce the notion of exact links, which admit Seifert surfaces with good homological conditions. We prove that for n >= 3, two exact (2n1)links are cobordant if they have such Seifert surfaces with algebraically cobordant Seifert forms. In particular, two fibered (2n1)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) 185205] 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 wellknown that a point T in cv_N in the (unprojectivized) CullerVogtmann 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 Horbit 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 HilbertSmith conjecture by Mahan Mj
We initiate a study of the topological group PPQI(G,H) of patternpreserving quasiisometries 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 patternpreserving uniform quasiisometries (or more generally any locally compact group of patternpreserving quasiisometries) 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 patternpreserving quasiisometries 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 patternpreserving 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 HilbertSmith conjecture for certain metric measure spaces, which uses the full strength of Yang's theorem on actions of the padic 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 3manifolds 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 conemanifold 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 4torus 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_1surjective branched cover T^n to N is a homeomorphism.
Geometry & Topology Publications is an imprint of Mathematical Sciences Publishers



