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Nine papers published by Geometry & Topology Publications
Posted:
Jan 10, 2013 12:22 PM


Eight papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 12 (2012) 21272178 A rank inequality for the knot Floer homology of double branched covers by Kristen Hendricks URL: http://www.msp.warwick.ac.uk/agt/2012/1204/p081.xhtml DOI: 10.2140/agt.2012.12.2127
(2) Algebraic & Geometric Topology 12 (2012) 21792244 A generalisation of the deformation variety by Henry Segerman URL: http://www.msp.warwick.ac.uk/agt/2012/1204/p082.xhtml DOI: 10.2140/agt.2012.12.2179
(3) Algebraic & Geometric Topology 12 (2012) 22452258 BourginYang version of the BorsukUlam theorem for Z_p^kequivariant maps by Waclaw Marzantowicz, Denise de Mattos and Edivaldo L dos Santos URL: http://www.msp.warwick.ac.uk/agt/2012/1204/p083.xhtml DOI: 10.2140/agt.2012.12.2245
(4) Algebraic & Geometric Topology 12 (2012) 22592286 On sections of hyperelliptic Lefschetz fibrations by Shunsuke Tanaka URL: http://www.msp.warwick.ac.uk/agt/2012/1204/p084.xhtml DOI: 10.2140/agt.2012.12.2259
(5) Algebraic & Geometric Topology 12 (2012) 22872297 The D(2)problem for dihedral groups of order 4n by Seamus O'Shea URL: http://www.msp.warwick.ac.uk/agt/2012/1204/p085.xhtml DOI: 10.2140/agt.2012.12.2287
(6) Algebraic & Geometric Topology 12 (2012) 22992316 Equivariant topological complexity by Hellen Colman and Mark Grant URL: http://www.msp.warwick.ac.uk/agt/2012/1204/p086.xhtml DOI: 10.2140/agt.2012.12.2299
(7) Algebraic & Geometric Topology 12 (2012) 23172327 Gromov Karea and jumping curves in CP^n by Yasha Savelyev URL: http://www.msp.warwick.ac.uk/agt/2012/1204/p087.xhtml DOI: 10.2140/agt.2012.12.2317
(8) Algebraic & Geometric Topology 12 (2012) 23292388 On the algebraic classification of module spectra by Irakli Patchkoria URL: http://www.msp.warwick.ac.uk/agt/2012/1204/p088.xhtml DOI: 10.2140/agt.2012.12.2329
One paper has been published by Geometry & Topology
(9) Geometry & Topology 16 (2012) 21712186 Onerelator Kahler groups by Indranil Biswas and Mahan Mj URL: http://www.msp.warwick.ac.uk/gt/2012/1604/p047.xhtml DOI: 10.2140/gt.2012.16.2171
Abstracts follow
(1) A rank inequality for the knot Floer homology of double branched covers by Kristen Hendricks
Given a knot K in S^3, let Sigma(K) be the double branched cover of S^3 over K. We show there is a spectral sequence whose E^1 page is (^HFK(Sigma(K),K) otimes V^{otimes(n1)}) otimes Z_2((q)), for V a Z_2vector space of dimension two, and whose E^{infinity} page is isomorphic to (^HFK(S^3,K) otimes V^{otimes(n1)}) otimes Z_2((q)), as Z_2((q))modules. As a consequence, we deduce a rank inequality between the knot Floer homologies ^HFK(Sigma(K),K) and ^HFK(S^3,K).
(2) A generalisation of the deformation variety by Henry Segerman
Given an ideal triangulation of a connected 3manifold with nonempty boundary consisting of a disjoint union of tori, a point of the deformation variety is an assignment of complex numbers to the dihedral angles of the tetrahedra subject to Thurston's gluing equations. From this, one can recover a representation of the fundamental group of the manifold into the isometries of 3dimensional hyperbolic space. However, the deformation variety depends crucially on the triangulation: there may be entire components of the representation variety which can be obtained from the deformation variety with one triangulation but not another. We introduce a generalisation of the deformation variety, which again consists of assignments of complex variables to certain dihedral angles subject to polynomial equations, but together with some extra combinatorial data concerning degenerate tetrahedra. This `extended deformation variety' deals with many situations that the deformation variety cannot. In particular we show that for any ideal triangulation of a small orientable 3manifold with a single torus boundary component, we can recover all of the irreducible nondihedral representations from the associated extended deformation variety. More generally, we give an algorithm to produce a triangulation of a given orientable 3manifold with torus boundary components for which the same result holds. As an application, we show that this extended deformation variety detects all factors of the PSL(2,C) Apolynomial associated to the components consisting of the representations it recovers.
(3) BourginYang version of the BorsukUlam theorem for Z_p^kequivariant maps by Waclaw Marzantowicz, Denise de Mattos and Edivaldo L dos Santos
Let G = Z_(p^k) be a cyclic group of prime power order and let V and W be orthogonal representations of G with V^G=W^G={0}. Let S(V) be the sphere of V and suppose f: S(V) > W is a Gequivariant mapping. We give an estimate for the dimension of the set f^{1}{0} in terms of V and W. This extends the BourginYang version of the BorsukUlam theorem to this class of groups. Using this estimate, we also estimate the size of the Gcoincidences set of a continuous map from S(V) into a real vector space W'.
(4) On sections of hyperelliptic Lefschetz fibrations by Shunsuke Tanaka
We construct a relation among righthanded Dehn twists in the mapping class group of a compact oriented surface of genus g with 4g+4 boundary components. This relation gives an explicit topological description of 4g+4 disjoint (1)sections of a hyperelliptic Lefschetz fibration of genus g on the manifold CP^2 #_(4g+5) CP^2bar.
(5) The D(2)problem for dihedral groups of order 4n by Seamus O'Shea
We give a full solution in terms of kinvariants of the D(2)problem for D_{4n}, assuming that Z[D_{4n}] satisfies torsionfree cancellation.
(6) Equivariant topological complexity by Hellen Colman and Mark Grant
We define and study an equivariant version of Farber's topological complexity for spaces with a given compact group action. This is a special case of the equivariant sectional category of an equivariant map, also defined in this paper. The relationship of these invariants with the equivariant LusternikSchnirelmann category is given. Several examples and computations serve to highlight the similarities and differences with the nonequivariant case. We also indicate how the equivariant topological complexity can be used to give estimates of the nonequivariant topological complexity.
(7) Gromov Karea and jumping curves in CP^n by Yasha Savelyev
We give here some extensions of Gromov's and Polterovich's theorems on karea of CP^n, particularly in the symplectic and Hamiltonian context. Our main methods involve GromovWitten theory, and some connections with Bott periodicity, and the theory of loop groups. The argument is closely connected with the study of jumping curves in CP^n, and as an upshot we prove a new symplecticgeometric theorem on these jumping curves.
(8) On the algebraic classification of module spectra by Irakli Patchkoria
Using methods developed by Franke in [Ktheory Preprint Archives 139 (1996)], we obtain algebraic classification results for modules over certain symmetric ring spectra (Salgebras). In particular, for any symmetric ring spectrum R whose graded homotopy ring pi_*(R) has graded global homological dimension 2 and is concentrated in degrees divisible by some natural number N >= 4, we prove that the homotopy category of Rmodules is equivalent to the derived category of the homotopy ring pi_*(R). This improves the BousfieldWolbert algebraic classification of isomorphism classes of objects of the homotopy category of Rmodules. The main examples of ring spectra to which our result applies are the plocal real connective Ktheory spectrum ko_(p), the JohnsonWilson spectrum E(2), and the truncated BrownPeterson spectrum BP<1>, all for an odd prime p. We also show that the equivalences for all these examples are exotic in the sense that they do not come from a zigzag of Quillen equivalences.
(9) Onerelator Kahler groups by Indranil Biswas and Mahan Mj
We prove that a onerelator group G is Kahler if and only if either G is finite cyclic or G is isomorphic to the fundamental group of a compact orbifold Riemann surface of genus g > 0 with at most one cone point of order n.
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