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 Geometry and Topology Posts: 140 Registered: 5/24/06
Posted: Mar 20, 2012 12:00 PM

(1) Algebraic & Geometric Topology 12 (2012) 131-153
Indecomposable PD_3-complexes
by Jonathan A Hillman
URL: http://www.msp.warwick.ac.uk/agt/2012/12-01/p008.xhtml
DOI: 10.2140/agt.2012.12.131

(2) Algebraic & Geometric Topology 12 (2012) 155-213
Locally symmetric spaces and K-theory of number fields
by Thilo Kuessner
URL: http://www.msp.warwick.ac.uk/agt/2012/12-01/p009.xhtml
DOI: 10.2140/agt.2012.12.155

(3) Algebraic & Geometric Topology 12 (2012) 215-233
On volumes of hyperbolic orbifolds
by Ilesanmi Adeboye and Guofang Wei
URL: http://www.msp.warwick.ac.uk/agt/2012/12-01/p010.xhtml
DOI: 10.2140/agt.2012.12.215

(4) Algebraic & Geometric Topology 12 (2012) 235-265
Generalized Mom-structures and ideal triangulations of 3-manifolds with nonspherical boundary
by Ekaterina Pervova
URL: http://www.msp.warwick.ac.uk/agt/2012/12-01/p011.xhtml
DOI: 10.2140/agt.2012.12.235

(5) Algebraic & Geometric Topology 12 (2012) 267-291
Lagrangian mapping class groups from a group homological point of view
by Takuya Sakasai
URL: http://www.msp.warwick.ac.uk/agt/2012/12-01/p012.xhtml
DOI: 10.2140/agt.2012.12.267

(6) Algebraic & Geometric Topology 12 (2012) 293-305
A note on Gornik's perturbation of Khovanov-Rozansky homology
by Andrew Lobb
URL: http://www.msp.warwick.ac.uk/agt/2012/12-01/p013.xhtml
DOI: 10.2140/agt.2012.12.293

(7) Algebraic & Geometric Topology 12 (2012) 307-342
Spectra associated to symmetric monoidal bicategories
by Angelica M Osorno
URL: http://www.msp.warwick.ac.uk/agt/2012/12-01/p014.xhtml
DOI: 10.2140/agt.2012.12.307

(8) Algebraic & Geometric Topology 12 (2012) 343-413
Higher cohomologies of modules
by Maria Calvo, Antonio M Cegarra and Nguyen T Quang
URL: http://www.msp.warwick.ac.uk/agt/2012/12-01/p015.xhtml
DOI: 10.2140/agt.2012.12.343

(9) Algebraic & Geometric Topology 12 (2012) 415-420
Noninjectivity of the hair'' map
by Bertrand Patureau-Mirand
URL: http://www.msp.warwick.ac.uk/agt/2012/12-01/p016.xhtml
DOI: 10.2140/agt.2012.12.415

(10) Algebraic & Geometric Topology 12 (2012) 421-433
Bounded orbits and global fixed points for groups acting on the plane
by Kathryn Mann
URL: http://www.msp.warwick.ac.uk/agt/2012/12-01/p017.xhtml
DOI: 10.2140/agt.2012.12.421

(11) Algebraic & Geometric Topology 12 (2012) 435-448
Lusternik-Schnirelmann category and the connectivity of X
by Nicholas A Scoville
URL: http://www.msp.warwick.ac.uk/agt/2012/12-01/p018.xhtml
DOI: 10.2140/agt.2012.12.435

(12) Algebraic & Geometric Topology 12 (2012) 449-467
Some bounds for the knot Floer au-invariant of satellite knots
by Lawrence P Roberts
URL: http://www.msp.warwick.ac.uk/agt/2012/12-01/p019.xhtml
DOI: 10.2140/agt.2012.12.449

(13) Algebraic & Geometric Topology 12 (2012) 469-492
Associahedra and weak monoidal structures on categories
by Zbigniew Fiedorowicz, Steven Gubkin and Rainer M Vogt
URL: http://www.msp.warwick.ac.uk/agt/2012/12-01/p020.xhtml
DOI: 10.2140/agt.2012.12.469

(14) Geometry & Topology 16 (2012) 391-432
A cohomological characterisation of Yu's property A for metric spaces
by Jacek Brodzki, Graham A Niblo and Nick Wright
URL: http://www.msp.warwick.ac.uk/gt/2012/16-01/p007.xhtml
DOI: 10.2140/gt.2012.16.391

(15) Geometry & Topology 16 (2012) 433-473
Chow rings and decomposition theorems for families of K!3 surfaces and Calabi-Yau hypersurfaces
by Claire Voisin
URL: http://www.msp.warwick.ac.uk/gt/2012/16-01/p008.xhtml
DOI: 10.2140/gt.2012.16.433

Abstracts follow

(1) Indecomposable PD_3-complexes
by Jonathan A Hillman

We show that if X is an indecomposable PD_3-complex and pi_1(X) is the
fundamental group of a reduced finite graph of finite groups but is
neither Z nor Z+Z/2Z then X is orientable, the underlying graph is a
tree, the vertex groups have cohomological period dividing 4 and all
but at most one of the edge groups is Z/2Z. If there are no
exceptions then all but at most one of the vertex groups is dihedral
of order 2m with m odd. Every such group is realized by some
PD_3-complex. Otherwise, one edge group may be Z/6Z. We do not know
of any such examples.

We also ask whether every PD_3-complex has a finite covering space
which is homotopy equivalent to a closed orientable 3-manifold, and we
propose a strategy for tackling this question.

(2) Locally symmetric spaces and K-theory of number fields
by Thilo Kuessner

For a closed locally symmetric space M=Gamma \ G/K and a
representation rho from G to GL(N,C) we consider the pushforward of
the fundamental class in H_*(BGL(overline{Q})) and a related invariant
in K_*(overline{Q}) otimes Q. We discuss the nontriviality of this
invariant and we generalize the construction to cusped locally
symmetric spaces of R-rank one.

(3) On volumes of hyperbolic orbifolds
by Ilesanmi Adeboye and Guofang Wei

We use HC Wang's bound on the radius of a ball embedded in the
fundamental domain of a lattice of a semisimple Lie group to construct an
explicit lower bound for the volume of a hyperbolic n-orbifold.

(4) Generalized Mom-structures and ideal triangulations of 3-manifolds with nonspherical boundary
by Ekaterina Pervova

The so-called Mom-structures on hyperbolic cusped 3-manifolds without
boundary were introduced by Gabai, Meyerhoff, and Milley, and used by
them to identify the smallest closed hyperbolic manifold. In this work
we extend the notion of a Mom-structure to include the case of
3-manifolds with nonempty boundary that does not have spherical
components. We then describe a certain relation between such
generalized Mom-structures, called protoMom-structures, internal on a
fixed 3-manifold N, and ideal triangulations of N; in addition, in the
case of nonclosed hyperbolic manifolds without annular cusps, we
describe how an internal geometric protoMom-structure can be
constructed starting from the Epstein--Penner or Kojima
decomposition. Finally, we exhibit a set of combinatorial moves that
relate any two internal protoMom-structures on a fixed N to each
other.

(5) Lagrangian mapping class groups from a group homological point of view
by Takuya Sakasai

We focus on two kinds of infinite index subgroups of the mapping class
group of a surface associated with a Lagrangian submodule of the first
homology of a surface. These subgroups, called Lagrangian mapping
class groups, are known to play important roles in the interaction
between the mapping class group and finite-type invariants of
3-manifolds. In this paper, we discuss these groups from a group
(co)homological point of view. The results include the determination
of their abelianizations, lower bounds of the second homology and
remarks on the (co)homology of higher degrees. As a byproduct of this
investigation, we determine the second homology of the mapping class
group of a surface of genus 3.

(6) A note on Gornik's perturbation of Khovanov-Rozansky homology
by Andrew Lobb

We show that the information contained in the associated graded vector
space to Gornik's version of Khovanov--Rozansky knot homology is
equivalent to a single even integer s_n(K). Furthermore we show that
s_n is a homomorphism from the smooth knot concordance group to the
integers. This is in analogy with Rasmussen's invariant coming from a
perturbation of Khovanov homology.

(7) Spectra associated to symmetric monoidal bicategories
by Angelica M Osorno

We show how to construct a Gamma-bicategory from a symmetric monoidal
bicategory and use that to show that the classifying space is an
infinite loop space upon group completion. We also show a way to
relate this construction to the classic Gamma-category construction
for a permutative category. As an example, we use this machinery to
construct a delooping of the K-theory of a rig category as defined by
Baas, Dundas and Rognes [London Math. Soc. Lecture Note Ser. 308,
Cambridge Univ. Press (2004) 18--45].

(8) Higher cohomologies of modules
by Maria Calvo, Antonio M Cegarra and Nguyen T Quang

If C is a small category, then a right C-module is a contravariant
functor from C into abelian groups. The abelian category Mod_C of
right C-modules has enough projective and injective objects, and the
groups Ext^n_Mod_C(B,A) provide the basic cohomology theory for
C-modules. In this paper we introduce, for each integer r>0, an
approach for a level-r cohomology theory for C-modules by defining
dedicated to. Applications to the homotopy classification of braided
and symmetric C-fibred categorical groups and their homomorphisms are
given.

(9) Noninjectivity of the hair'' map
by Bertrand Patureau-Mirand

Kricker constructed a knot invariant Z^rat valued in a space of
Feynman diagrams with beads. When composed with the "hair" map H, it
gives the Kontsevich integral of the knot. We introduce a new grading
on diagrams with beads and use it to show that a nontrivial element
constructed from Vogel's zero divisor in the algebra Lambda is in the
kernel of H. This shows that H is not injective.

(10) Bounded orbits and global fixed points for groups acting on the plane
by Kathryn Mann

Let G be a group acting on the plane by orientation-preserving
homeomorphisms. We show that a tight bound on orbits implies a global
fixed point. Precisely, if for some k>0 there is a ball of radius r >
(1/sqrt{3})k such that each point x in the ball satisfies ||g(x) -
h(x)||<=k for all g, h in G, and the action of G satisfies a
nonwandering hypothesis, then the action has a global fixed point. In
particular any group of measure-preserving, orientation-preserving
homeomorphisms of the plane with uniformly bounded orbits has a global
fixed point. The constant (1/sqrt{3})k is sharp.

As an application, we also show that a group acting on the plane by
diffeomorphisms with orbits bounded as above is left orderable.

(11) Lusternik-Schnirelmann category and the connectivity of X
by Nicholas A Scoville

We define and study a homotopy invariant called the connectivity
weight to compute the weighted length between spaces X and Y. This is
an invariant based on the connectivity of A_i, where A_i is a space
attached in a mapping cone sequence from X to Y. We use the
Lusternik-Schnirelmann category to prove a theorem concerning the
connectivity of all spaces attached in any decomposition from X to Y.
This theorem is used to prove that for any positive rational number q,
there is a space X such that q=cl^{omega}(X), the connectivity
weighted cone-length of X. We compute cl^{omega}(X) and kl^{omega}(X)
for many spaces and give several examples.

(12) Some bounds for the knot Floer au-invariant of satellite knots
by Lawrence P Roberts

This paper uses four dimensional handlebody theory to compute upper and lower
bounds for the Heegaard Floer tau-invariant of almost all satellite knots in
terms of the tau-invariants of the pattern and the companion.

(13) Associahedra and weak monoidal structures on categories
by Zbigniew Fiedorowicz, Steven Gubkin and Rainer M Vogt

This paper answers the following question: what algebraic structure on
a category corresponds to an A_n structure (in the sense of Stasheff)
on the geometric realization of its nerve?

(14) A cohomological characterisation of Yu's property A for metric spaces
by Jacek Brodzki, Graham A Niblo and Nick Wright

We develop a new framework for cohomology of discrete metric spaces
and groups which simultaneously generalises group cohomology, Roe's
coarse cohomology, Gersten's \ell^\infty-cohomology and Johnson's
bounded cohomology. In this framework we give an answer to Higson's
question concerning the existence of a cohomological characterisation
of Yu's property A, analogous to Johnson's characterisation of
amenability. In particular, we introduce an analogue of invariant
mean for metric spaces with property A. As an application we extend
Guentner's result that box spaces of a finitely generated group have
property A if and only if the group is amenable. This provides an
alternative proof of Nowak's result that the infinite dimensional cube
does not have property A.

(15) Chow rings and decomposition theorems for families of K!3 surfaces and Calabi-Yau hypersurfaces
by Claire Voisin

The decomposition theorem for smooth projective morphisms pi: X->B
says that Rpi_*Q decomposes as a direct sum of R^i pi_*Q[-i]. We
describe simple examples where it is not possible to have such a
decomposition compatible with cup product, even after restriction to
Zariski dense open sets of B. We prove however that this is always
possible for families of K3 surfaces (after shrinking the base), and
show how this result relates to a result by Beauville and the author
[J. Algebraic Geom. 13 (2004) 417--426] on the Chow ring of a K3
surface S. We give two proofs of this result, the first one involving
K-autocorrespondences of K3 surfaces, seen as analogues of isogenies
of abelian varieties, the second one involving a certain decomposition
of the small diagonal in S^3 obtained by Beauville and the author. We
also prove an analogue of such a decomposition of the small diagonal
in X^3 for Calabi--Yau hypersurfaces X in P^n, which in turn provides
strong restrictions on their Chow ring.

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