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Nine papers published by Geometry & Topology Publications
Posted:
Jan 10, 2013 12:22 PM
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Eight papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 12 (2012) 2127-2178
A rank inequality for the knot Floer homology of double branched
covers
by Kristen Hendricks
URL: http://www.msp.warwick.ac.uk/agt/2012/12-04/p081.xhtml
DOI: 10.2140/agt.2012.12.2127
(2) Algebraic & Geometric Topology 12 (2012) 2179-2244
A generalisation of the deformation variety
by Henry Segerman
URL: http://www.msp.warwick.ac.uk/agt/2012/12-04/p082.xhtml
DOI: 10.2140/agt.2012.12.2179
(3) Algebraic & Geometric Topology 12 (2012) 2245-2258
Bourgin-Yang version of the Borsuk-Ulam theorem for
Z_p^k-equivariant maps
by Waclaw Marzantowicz, Denise de Mattos and Edivaldo L dos Santos
URL: http://www.msp.warwick.ac.uk/agt/2012/12-04/p083.xhtml
DOI: 10.2140/agt.2012.12.2245
(4) Algebraic & Geometric Topology 12 (2012) 2259-2286
On sections of hyperelliptic Lefschetz fibrations
by Shunsuke Tanaka
URL: http://www.msp.warwick.ac.uk/agt/2012/12-04/p084.xhtml
DOI: 10.2140/agt.2012.12.2259
(5) Algebraic & Geometric Topology 12 (2012) 2287-2297
The D(2)-problem for dihedral groups of order 4n
by Seamus O'Shea
URL: http://www.msp.warwick.ac.uk/agt/2012/12-04/p085.xhtml
DOI: 10.2140/agt.2012.12.2287
(6) Algebraic & Geometric Topology 12 (2012) 2299-2316
Equivariant topological complexity
by Hellen Colman and Mark Grant
URL: http://www.msp.warwick.ac.uk/agt/2012/12-04/p086.xhtml
DOI: 10.2140/agt.2012.12.2299
(7) Algebraic & Geometric Topology 12 (2012) 2317-2327
Gromov K-area and jumping curves in CP^n
by Yasha Savelyev
URL: http://www.msp.warwick.ac.uk/agt/2012/12-04/p087.xhtml
DOI: 10.2140/agt.2012.12.2317
(8) Algebraic & Geometric Topology 12 (2012) 2329-2388
On the algebraic classification of module spectra
by Irakli Patchkoria
URL: http://www.msp.warwick.ac.uk/agt/2012/12-04/p088.xhtml
DOI: 10.2140/agt.2012.12.2329
One paper has been published by Geometry & Topology
(9) Geometry & Topology 16 (2012) 2171-2186
One-relator Kahler groups
by Indranil Biswas and Mahan Mj
URL: http://www.msp.warwick.ac.uk/gt/2012/16-04/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(n-1)}) otimes Z_2((q)), for V a
Z_2-vector space of dimension two, and whose E^{infinity} page is
isomorphic to (^HFK(S^3,K) otimes V^{otimes(n-1)}) 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 3-manifold 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
3-dimensional 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 3-manifold 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 3-manifold 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) A-polynomial
associated to the components consisting of the representations it
recovers.
(3) Bourgin-Yang version of the Borsuk-Ulam theorem for
Z_p^k-equivariant 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 G-equivariant mapping. We
give an estimate for the dimension of the set f^{-1}{0} in terms of V
and W. This extends the Bourgin-Yang version of the Borsuk-Ulam
theorem to this class of groups. Using this estimate, we also
estimate the size of the G-coincidences 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 right-handed 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^2-bar.
(5) The D(2)-problem for dihedral groups of order 4n
by Seamus O'Shea
We give a full solution in terms of k-invariants of the D(2)-problem
for D_{4n}, assuming that Z[D_{4n}] satisfies torsion-free
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 Lusternik-Schnirelmann 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 K-area and jumping curves in CP^n
by Yasha Savelyev
We give here some extensions of Gromov's and Polterovich's theorems on
k-area of CP^n, particularly in the symplectic and Hamiltonian
context. Our main methods involve Gromov-Witten 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 symplectic-geometric theorem on
these jumping curves.
(8) On the algebraic classification of module spectra
by Irakli Patchkoria
Using methods developed by Franke in [K-theory Preprint Archives 139
(1996)], we obtain algebraic classification results for modules over
certain symmetric ring spectra (S-algebras). 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 R-modules is equivalent to the derived category of the
homotopy ring pi_*(R). This improves the Bousfield-Wolbert algebraic
classification of isomorphism classes of objects of the homotopy
category of R-modules. The main examples of ring spectra to which our
result applies are the p-local real connective K-theory spectrum
ko_(p), the Johnson-Wilson spectrum E(2), and the truncated
Brown-Peterson 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) One-relator Kahler groups
by Indranil Biswas and Mahan Mj
We prove that a one-relator 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.
Geometry & Topology Publications is an imprint of
Mathematical Sciences Publishers
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