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Nine papers and a monograph published by Geometry & Topology Publications
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Nine papers and a monograph published by Geometry & Topology Publications
Posted:
Jun 22, 2013 8:54 AM


The online version of Geometry & Topology Monographs Volume 18:
Proceedings of the Freedman Fest ================================ Editors: Rob Kirby, Vyacheslav Krushkal and Zhenghan Wang
is now complete at: http://msp.warwick.ac.uk/gtm/2012/18/
Four papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 13 (2013) 22072238 Cohomology of KacMoody groups over a finite field by Jaume Aguade and Albert Ruiz URL: http://www.msp.warwick.ac.uk/agt/2013/1304/p070.xhtml DOI: 10.2140/agt.2013.13.2207
(2) Algebraic & Geometric Topology 13 (2013) 22392260 The absolute gradings on embedded contact homology and SeibergWitten Floer cohomology by Daniel CristofaroGardiner URL: http://www.msp.warwick.ac.uk/agt/2013/1304/p071.xhtml DOI: 10.2140/agt.2013.13.2239
(3) Algebraic & Geometric Topology 13 (2013) 22612282 Embedding relatively hyperbolic groups in products of trees by John M Mackay and Alessandro Sisto URL: http://www.msp.warwick.ac.uk/agt/2013/1304/p072.xhtml DOI: 10.2140/agt.2013.13.2261
(4) Algebraic & Geometric Topology 13 (2013) 22832316 A finitedimensional approach to the strong Novikov conjecture by Daniel Ramras, Rufus Willett and Guoliang Yu URL: http://www.msp.warwick.ac.uk/agt/2013/1304/p073.xhtml DOI: 10.2140/agt.2013.13.2283
Five papers have been published by Geometry & Topology
(5) Geometry & Topology 17 (2013) 14971534 Intersections of quadrics, momentangle manifolds and connected sums by Samuel Gitler and Santiago Lopez de Medrano URL: http://www.msp.warwick.ac.uk/gt/2013/1703/p034.xhtml DOI: 10.2140/gt.2013.17.1497
(6) Geometry & Topology 17 (2013) 15351579 Lipschitz retraction and distortion for subgroups of Out(F_n) by Michael Handel and Lee Mosher URL: http://www.msp.warwick.ac.uk/gt/2013/1703/p035.xhtml DOI: 10.2140/gt.2013.17.1535
(7) Geometry & Topology 17 (2013) 15811670 The free splitting complex of a free group, I: hyperbolicity by Michael Handel and Lee Mosher URL: http://www.msp.warwick.ac.uk/gt/2013/1703/p036.xhtml DOI: 10.2140/gt.2013.17.1581
(8) Geometry & Topology 17 (2013) 16711706 Motivic BrownPeterson invariants of the rationals by Kyle M Ormsby and Paul Arne Ostvaer URL: http://www.msp.warwick.ac.uk/gt/2013/1703/p037.xhtml DOI: 10.2140/gt.2013.17.1671
(9) Geometry & Topology 17 (2013) 17071744 Random rigidity in the free group by Danny Calegari and Alden Walker URL: http://www.msp.warwick.ac.uk/gt/2013/1703/p038.xhtml DOI: 10.2140/gt.2013.17.1707
Abstracts follow
(1) Cohomology of KacMoody groups over a finite field by Jaume Aguade and Albert Ruiz
We compute the mod p cohomology algebra of a family of infinite discrete KacMoody groups of rank two defined over finite fields of characteristic different from p.
(2) The absolute gradings on embedded contact homology and SeibergWitten Floer cohomology by Daniel CristofaroGardiner
Let Y be a closed connected contact 3manifold. In [Geom. Topol. 14 (2010) 24972581], Taubes defines an isomorphism between the embedded contact homology (ECH) of Y and its SeibergWitten Floer cohomology. Both the ECH of Y and the SeibergWitten Floer cohomology of Y admit absolute gradings by homotopy classes of oriented 2plane fields. We show that Taubes' isomorphism preserves these gradings, which implies that the absolute grading on ECH is a topological invariant. To do this, we prove another result relating the expected dimension of any component of the SeibergWitten moduli space over a completed connected symplectic cobordism to the ECH index of a corresponding homology class.
(3) Embedding relatively hyperbolic groups in products of trees by John M Mackay and Alessandro Sisto
We show that a relatively hyperbolic group quasiisometrically embeds in a product of finitely many trees if the peripheral subgroups do, and we provide an estimate on the minimal number of trees needed. Applying our result to the case of 3manifolds, we show that fundamental groups of closed 3manifolds have linearly controlled asymptotic dimension at most 8. To complement this result, we observe that fundamental groups of Haken 3manifolds with nonempty boundary have asymptotic dimension 2.
(4) A finitedimensional approach to the strong Novikov conjecture by Daniel Ramras, Rufus Willett and Guoliang Yu
The aim of this paper is to describe an approach to the (strong) Novikov conjecture based on continuous families of finitedimensional representations: this is partly inspired by ideas of Lusztig related to the AtiyahSinger families index theorem, and partly by Carlsson's deformation Ktheory. Using this approach, we give new proofs of the strong Novikov conjecture in several interesting cases, including crystallographic groups and surface groups. The method presented here is relatively accessible compared with other proofs of the Novikov conjecture, and also yields some information about the Ktheory and cohomology of representation spaces.
(5) Intersections of quadrics, momentangle manifolds and connected sums by Samuel Gitler and Santiago Lopez de Medrano
For the intersections of real quadrics in R^n and in C^n associated to simple polytopes (also known as universal abelian covers and momentangle manifolds, respectively) we obtain the following results: (1) Every such manifold of dimension greater than or equal to 5, connected up to the middle dimension and with free homology is diffeomorphic to a connected sum of sphere products. The same is true for the manifolds in infinite families stemming from each of them. This includes the momentangle manifolds for which he result was conjectured by F Bosio and L Meersseman. (2) The topological effect on the manifolds of cutting off vertices and edges from the polytope is described. Combined with the result in (1), this gives the same result for many more natural, infinite families. (3) As a consequence of (2), the cohomology rings of the two manifolds associated to a polytope need not be isomorphic, contradicting published results about complements of arrangements. (4) Auxiliary but general constructions and results in Geometric Topology.
(6) Lipschitz retraction and distortion for subgroups of Out(F_n) by Michael Handel and Lee Mosher
Given a free factor A of the rank n free group F_n, we characterize when the subgroup of Out(F_n) that stabilizes the conjugacy class of A is distorted in Out(F_n). We also prove that the image of the natural embedding of Aut(F_{n1}) in Aut(F_n) is nondistorted, that the stabilizer in Out(F_n) of the conjugacy class of any free splitting of F_n is nondistorted and we characterize when the stabilizer of the conjugacy class of an arbitrary free factor system of F_n is distorted. In all proofs of nondistortion, we prove the stronger statement that the subgroup in question is a Lipschitz retract. As applications we determine Dehn functions and automaticity for Out(F_n) and Aut(F_n).
(7) The free splitting complex of a free group, I: hyperbolicity by Michael Handel and Lee Mosher
We prove that the free splitting complex of a finite rank free group, also known as Hatcher's sphere complex, is hyperbolic.
(8) Motivic BrownPeterson invariants of the rationals by Kyle M Ormsby and Paul Arne Ostvaer
Let BP<n>, n at least 0 and at most infinity, denote the family of motivic truncated BrownPeterson spectra over Q. We employ a `localtoglobal' philosophy in order to compute the bigraded homotopy groups of BP<n>. Along the way, we produce a computation of the homotopy groups of BP<n> over Q_2, prove a motivic Hasse principle for the spectra BP<n>, and reprove several classical and recent theorems about the Ktheory of particular fields in a streamlined fashion. We also compute the bigraded homotopy groups of the 2complete algebraic cobordism spectrum MGL over Q.
(9) Random rigidity in the free group by Danny Calegari and Alden Walker
We prove a rigidity theorem for the geometry of the unit ball in random subspaces of the scl norm in B_1^H of a free group. In a free group F of rank k, a random word w of length n (conditioned to lie in [F,F]) has scl(w) = log(2k1)n / 6 log(n) + o(n / log(n)) with high probability, and the unit ball in a subspace spanned by d random words of length O(n) is C^0 close to a (suitably affinely scaled) octahedron. A conjectural generalization to hyperbolic groups and manifolds (discussed in the appendix) would show that the length of a random geodesic in a hyperbolic manifold can be recovered from the bounded cohomology of the fundamental group.
Geometry & Topology Publications is an imprint of Mathematical Sciences Publishers



