Thirteen papers published by Geometry & Topology Publications

[Geometry and Topology]

Ten papers have been published by Algebraic & Geometric Topology

(1) Algebraic & Geometric Topology 13 (2013) 1513-1530
���Centralizers of finite subgroups �of the mapping class group
�����by Hao Liang
���URL: http://www.msp.warwick.ac.uk/agt/2013/13-03/p048.xhtml
���DOI: 10.2140/agt.2013.13.1513

(2) Algebraic & Geometric Topology 13 (2013) 1531-1578
���A geometric construction of panel-regular lattices �
���for buildings of types wtilde A_2 and wtilde C_2
�����by Jan Essert
���URL: http://www.msp.warwick.ac.uk/agt/2013/13-03/p049.xhtml
���DOI: 10.2140/agt.2013.13.1531

(3) Algebraic & Geometric Topology 13 (2013) 1579-1612
���Some Ramsey-type results on �intrinsic linking of n-complexes
�����by Christopher Tuffley
���URL: http://www.msp.warwick.ac.uk/agt/2013/13-03/p050.xhtml
���DOI: 10.2140/agt.2013.13.1579

(4) Algebraic & Geometric Topology 13 (2013) 1613-1660
���Contact surgery and supporting open books
�����by Russell Avdek
���URL: http://www.msp.warwick.ac.uk/agt/2013/13-03/p051.xhtml
���DOI: 10.2140/agt.2013.13.1613

(5) Algebraic & Geometric Topology 13 (2013) 1661-1708
���Integral cohomology of rational projection method patterns
�����by Franz Gaehler, John Hunton and Johannes Kellendonk
���URL: http://www.msp.warwick.ac.uk/agt/2013/13-03/p052.xhtml
���DOI: 10.2140/agt.2013.13.1661

(6) Algebraic & Geometric Topology 13 (2013) 1709-1731
���Singular maps on exotic 4-manifold pairs
�����by Boldizsar Kalmar and Andras I Stipsicz
���URL: http://www.msp.warwick.ac.uk/agt/2013/13-03/p053.xhtml
���DOI: 10.2140/agt.2013.13.1709

(7) Algebraic & Geometric Topology 13 (2013) 1733-1742
���Milnor-Wood inequalities for products
�����by Michelle Bucher and Tsachik Gelander
���URL: http://www.msp.warwick.ac.uk/agt/2013/13-03/p054.xhtml
���DOI: 10.2140/agt.2013.13.1733

(8) Algebraic & Geometric Topology 13 (2013) 1743-1755
���On the slice spectral sequence
�����by John Ullman
���URL: http://www.msp.warwick.ac.uk/agt/2013/13-03/p055.xhtml
���DOI: 10.2140/agt.2013.13.1743

(9) Algebraic & Geometric Topology 13 (2013) 1757-1778
���Mod p decompositions of gauge groups
�����by Daisuke Kishimoto, Akira Kono and Mitsunobu Tsutaya
���URL: http://www.msp.warwick.ac.uk/agt/2013/13-03/p056.xhtml
���DOI: 10.2140/agt.2013.13.1757

(10) Algebraic & Geometric Topology 13 (2013) 1779-1813
���Fibre sequences and localization of simplicial sheaves
�����by Matthias Wendt
���URL: http://www.msp.warwick.ac.uk/agt/2013/13-03/p057.xhtml
���DOI: 10.2140/agt.2013.13.1779

Three papers have been published by Geometry & Topology

(11) Geometry & Topology 17 (2013) 1113-1147
���Betti numbers of finite volume orbifolds
�����by Iddo Samet
���URL: http://www.msp.warwick.ac.uk/gt/2013/17-02/p024.xhtml
���DOI: 10.2140/gt.2013.17.1113

(12) Geometry & Topology 17 (2013) 1149-1163
���Poincare invariants are Seiberg-Witten invariants
�����by Huai-liang Chang and Young-Hoon Kiem
���URL: http://www.msp.warwick.ac.uk/gt/2013/17-02/p025.xhtml
���DOI: 10.2140/gt.2013.17.1149

(13) Geometry & Topology 17 (2013) 1165-1198
���Characteristic classes of Hilbert schemes of points
���via symmetric products
�����by Sylvain Cappell, Laurentiu Maxim, Toru Ohmoto,
��������Joerg Schuermann and Shoji Yokura
���URL: http://www.msp.warwick.ac.uk/gt/2013/17-02/p026.xhtml
���DOI: 10.2140/gt.2013.17.1165

Abstracts follow

(1) Centralizers of finite subgroups �of the mapping class group
�����by Hao Liang

In this paper, we study the action of finite subgroups of the mapping
class group of a surface on the curve complex. We prove that if the
diameter of the almost fixed point set of a finite subgroup H is big
enough, then the centralizer of H is infinite.


(2) A geometric construction of panel-regular lattices �
���for buildings of types wtilde A_2 and wtilde C_2
�����by Jan Essert

Using Singer polygons, we construct locally finite affine buildings of
types \tilde{A}_2 and \tilde{C}_2 that admit uniform lattices acting
regularly on panels. For type \tilde{A}_2, these cover all possible
buildings admitting panel-regular lattices. All but one of the
\tilde{C}_2-buildings are necessarily exotic. To the knowledge of the
author, these are the first presentations of lattices for buildings of
type \tilde{C}_2. Integral and rational group homology for the
lattices is also calculated.


(3) Some Ramsey-type results on �intrinsic linking of n-complexes
�����by Christopher Tuffley

Define the complete n-complex on N vertices to be the n-skeleton of an
(N-1)-simplex. �We show that embeddings of sufficiently large complete
n-complexes in R^{2n+1} necessarily exhibit complicated linking
behaviour, thereby extending known results on embeddings of large
complete graphs in R^3 (the case n=1) to higher dimensions. In
particular, we prove the existence of links of the following types:
r-component links, with the linking pattern of a chain, necklace or
keyring; 2-component links with linking number at least lambda in
absolute value; and 2-component links with linking number a nonzero
multiple of a given integer q. For fixed n the number of vertices
required for each of our results grows at most polynomially with
respect to the parameter r, lambda or q.


(4) Contact surgery and supporting open books
�����by Russell Avdek

Let (M,xi) be a contact 3--manifold. �We present two new algorithms,
the first of which converts an open book (Sigma,Phi) supporting (M,xi)
with connected binding into a contact surgery diagram. �The second
turns a contact surgery diagram for (M,xi) into a supporting open book
decomposition. �These constructions lead to a refinement of a result
of Ding and Geiges [Math. Proc. Cambridge Philos. Soc. 136 (2004)
583--598], which states that every such (M,xi) may be obtained by
contact surgery from (S^3,xi_{std}), as well as bounds on the support
norm and genus (Etnyre and Ozbagci [Trans. Amer. Math. Soc. 360 (2008)
3133--3151]) of contact manifolds obtained by surgery in terms of
classical link data. �We then introduce Kirby moves called ribbon
moves, which use mapping class relations to modify contact surgery
diagrams. �Any two surgery diagrams of the same contact 3--manifold
are related by a sequence of Legendrian isotopies and ribbon moves.
As most of our results are computational in nature, a number of
examples are analyzed.


(5) Integral cohomology of rational projection method patterns
�����by Franz Gaehler, John Hunton and Johannes Kellendonk

We study the cohomology and hence K-theory of the aperiodic tilings
formed by the so called "cut and project" method, that is, patterns in
d-dimensional Euclidean space which arise as sections of higher
dimensional, periodic structures. They form one of the key families of
patterns used in quasicrystal physics, where their topological
invariants carry quantum mechanical information. Our work develops
both a theoretical framework and a practical toolkit for the
discussion and calculation of their integral cohomology, and extends
previous work that only successfully addressed rational cohomological
invariants. Our framework unifies the several previous methods used to
study the cohomology of these patterns. We discuss explicit
calculations for the main examples of icosahedral patterns in R^3 --
the Danzer tiling, the Ammann-Kramer tiling and the Canonical and
Dual Canonical D_6 tilings, including complete computations for the
first of these, as well as results for many of the better known
2-dimensional examples.


(6) Singular maps on exotic 4-manifold pairs
�����by Boldizsar Kalmar and Andras I Stipsicz

We show examples of pairs of smooth, compact, homeomorphic
4-manifolds, whose diffeomorphism types are distinguished by the
topology of the singular sets of smooth stable maps defined on them.
In this distinction we rely on results from Seiberg-Witten theory.


(7) Milnor-Wood inequalities for products
�����by Michelle Bucher and Tsachik Gelander

We prove Milnor-Wood inequalities for local products of manifolds. As
a consequence, we establish the generalized Chern conjecture for
products M times Sigma^k of any manifold M and k copies of a surface
Sigma for k sufficiently large.


(8) On the slice spectral sequence
�����by John Ullman

We introduce a variant of the slice spectral sequence which uses only
regular slice cells, and state the precise relationship between the
two spectral sequences. We analyze how the slice filtration of an
equivariant spectrum that is concentrated over a normal subgroup is
related to the slice filtration of its geometric fixed points, and use
this to prove a conjecture of Hill on the slice filtration of an
Eilenberg-MacLane spectrum (arXiv:1107.3582v1). We also show how the
(co)connectivity of a spectrum results in the (co)connectivity of its
slice tower, demonstrating the `efficiency' of the slice spectral
sequence.


(9) Mod p decompositions of gauge groups
�����by Daisuke Kishimoto, Akira Kono and Mitsunobu Tsutaya

We give mod p decompositions of homotopy types of the gauge groups of
principal bundles over spheres, which are compatible with mod p
decompositions of Lie groups given by Mimura, Nishida and Toda. �As an
application, we also give some computations on the homotopy types of
gauge groups. �In particular, we show the p-local converse of the
result of Sutherland on the classifications of the gauge groups of
principal SU(n)-bundles.


(10) Fibre sequences and localization of simplicial sheaves
�����by Matthias Wendt

In this paper, we discuss the theory of quasifibrations in proper
Bousfield localizations of model categories of simplicial sheaves. �We
provide a construction of fibrewise localization and use this
construction to generalize a criterion for locality of fibre sequences
due to Berrick and Dror Farjoun. The results allow a better
understanding of unstable A^1-homotopy theory.


(11) Betti numbers of finite volume orbifolds
�����by Iddo Samet

We prove that the Betti numbers of a negatively curved orbifold are
linearly bounded by its volume, generalizing a theorem of Gromov that
establishes this bound for manifolds. �An immediate corollary is that
Betti numbers of a lattice in a rank-one Lie group are linearly
bounded by its co-volume.


(12) Poincare invariants are Seiberg-Witten invariants
�����by Huai-liang Chang and Young-Hoon Kiem

We prove a conjecture of Duerr, Kabanov and Okonek that provides an
algebro-geometric theory of Seiberg-Witten invariants for all smooth
projective surfaces. �Our main technique is the cosection localization
principle (Kiem and Li [arXiv:1007.3085]) of virtual cycles.


(13) Characteristic classes of Hilbert schemes of points
����via symmetric products
�����by Sylvain Cappell, Laurentiu Maxim, Toru Ohmoto,
��������Joerg Schuermann and Shoji Yokura

We obtain a formula for the generating series of (the push-forward
under the Hilbert-Chow morphism of) the Hirzebruch homology
characteristic classes of the Hilbert schemes of points for a smooth
quasi-projective variety of arbitrary pure dimension. This result is
based on a geometric construction of a motivic exponentiation
generalizing the notion of motivic power structure, as well as on a
formula for the generating series of the Hirzebruch homology
characteristic classes of symmetric products. We apply the same
methods for the calculation of generating series formulae for the
Hirzebruch classes of the push-forwards of "virtual motives" of
Hilbert schemes of a threefold. As corollaries, we obtain counterparts
for the MacPherson (and Aluffi) Chern classes of Hilbert schemes of a
smooth quasi-projective variety (resp. for threefolds). For a
projective Calabi-Yau threefold, the latter yields a Chern class
version of the dimension zero MNOP conjecture.



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