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Thirteen papers published by Geometry & Topology Publications
Posted:
May 19, 2013 8:32 PM


Ten papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 13 (2013) 15131530 Centralizers of finite subgroups of the mapping class group by Hao Liang URL: http://www.msp.warwick.ac.uk/agt/2013/1303/p048.xhtml DOI: 10.2140/agt.2013.13.1513
(2) Algebraic & Geometric Topology 13 (2013) 15311578 A geometric construction of panelregular lattices for buildings of types wtilde A_2 and wtilde C_2 by Jan Essert URL: http://www.msp.warwick.ac.uk/agt/2013/1303/p049.xhtml DOI: 10.2140/agt.2013.13.1531
(3) Algebraic & Geometric Topology 13 (2013) 15791612 Some Ramseytype results on intrinsic linking of ncomplexes by Christopher Tuffley URL: http://www.msp.warwick.ac.uk/agt/2013/1303/p050.xhtml DOI: 10.2140/agt.2013.13.1579
(4) Algebraic & Geometric Topology 13 (2013) 16131660 Contact surgery and supporting open books by Russell Avdek URL: http://www.msp.warwick.ac.uk/agt/2013/1303/p051.xhtml DOI: 10.2140/agt.2013.13.1613
(5) Algebraic & Geometric Topology 13 (2013) 16611708 Integral cohomology of rational projection method patterns by Franz Gaehler, John Hunton and Johannes Kellendonk URL: http://www.msp.warwick.ac.uk/agt/2013/1303/p052.xhtml DOI: 10.2140/agt.2013.13.1661
(6) Algebraic & Geometric Topology 13 (2013) 17091731 Singular maps on exotic 4manifold pairs by Boldizsar Kalmar and Andras I Stipsicz URL: http://www.msp.warwick.ac.uk/agt/2013/1303/p053.xhtml DOI: 10.2140/agt.2013.13.1709
(7) Algebraic & Geometric Topology 13 (2013) 17331742 MilnorWood inequalities for products by Michelle Bucher and Tsachik Gelander URL: http://www.msp.warwick.ac.uk/agt/2013/1303/p054.xhtml DOI: 10.2140/agt.2013.13.1733
(8) Algebraic & Geometric Topology 13 (2013) 17431755 On the slice spectral sequence by John Ullman URL: http://www.msp.warwick.ac.uk/agt/2013/1303/p055.xhtml DOI: 10.2140/agt.2013.13.1743
(9) Algebraic & Geometric Topology 13 (2013) 17571778 Mod p decompositions of gauge groups by Daisuke Kishimoto, Akira Kono and Mitsunobu Tsutaya URL: http://www.msp.warwick.ac.uk/agt/2013/1303/p056.xhtml DOI: 10.2140/agt.2013.13.1757
(10) Algebraic & Geometric Topology 13 (2013) 17791813 Fibre sequences and localization of simplicial sheaves by Matthias Wendt URL: http://www.msp.warwick.ac.uk/agt/2013/1303/p057.xhtml DOI: 10.2140/agt.2013.13.1779
Three papers have been published by Geometry & Topology
(11) Geometry & Topology 17 (2013) 11131147 Betti numbers of finite volume orbifolds by Iddo Samet URL: http://www.msp.warwick.ac.uk/gt/2013/1702/p024.xhtml DOI: 10.2140/gt.2013.17.1113
(12) Geometry & Topology 17 (2013) 11491163 Poincare invariants are SeibergWitten invariants by Huailiang Chang and YoungHoon Kiem URL: http://www.msp.warwick.ac.uk/gt/2013/1702/p025.xhtml DOI: 10.2140/gt.2013.17.1149
(13) Geometry & Topology 17 (2013) 11651198 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/2013/1702/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 panelregular 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 panelregular lattices. All but one of the \tilde{C}_2buildings 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 Ramseytype results on intrinsic linking of ncomplexes by Christopher Tuffley
Define the complete ncomplex on N vertices to be the nskeleton of an (N1)simplex. We show that embeddings of sufficiently large complete ncomplexes 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: rcomponent links, with the linking pattern of a chain, necklace or keyring; 2component links with linking number at least lambda in absolute value; and 2component 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 3manifold. 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) 583598], 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) 31333151]) 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 3manifold 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 Ktheory of the aperiodic tilings formed by the so called "cut and project" method, that is, patterns in ddimensional 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 AmmannKramer 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 2dimensional examples.
(6) Singular maps on exotic 4manifold pairs by Boldizsar Kalmar and Andras I Stipsicz
We show examples of pairs of smooth, compact, homeomorphic 4manifolds, 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 SeibergWitten theory.
(7) MilnorWood inequalities for products by Michelle Bucher and Tsachik Gelander
We prove MilnorWood 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 EilenbergMacLane 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 plocal 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^1homotopy 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 rankone Lie group are linearly bounded by its covolume.
(12) Poincare invariants are SeibergWitten invariants by Huailiang Chang and YoungHoon Kiem
We prove a conjecture of Duerr, Kabanov and Okonek that provides an algebrogeometric theory of SeibergWitten 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 pushforward under the HilbertChow morphism of) the Hirzebruch homology characteristic classes of the Hilbert schemes of points for a smooth quasiprojective 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 pushforwards 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 quasiprojective variety (resp. for threefolds). For a projective CalabiYau threefold, the latter yields a Chern class version of the dimension zero MNOP conjecture.
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