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Nine papers published by Geometry & Topology Publications
Posted:
Oct 15, 2011 9:35 AM


Four papers have been published by Algebraic & Geometric Topology:
(1) Algebraic & Geometric Topology 11 (2011) 27752814 Deltadiscrete Gspectra and iterated homotopy fixed points by Daniel G Davis URL: http://www.msp.warwick.ac.uk/agt/2011/1105/p089.xhtml DOI: 10.2140/agt.2011.11.2775
(2) Algebraic & Geometric Topology 11 (2011) 28152827 A loop theorem/Dehn's lemma for some orbifolds by Josh Barnard URL: http://www.msp.warwick.ac.uk/agt/2011/1105/p090.xhtml DOI: 10.2140/agt.2011.11.2815
(3) Algebraic & Geometric Topology 11 (2011) 28292860 Spectral sequences in string topology by Lennart Meier URL: http://www.msp.warwick.ac.uk/agt/2011/1105/p091.xhtml DOI: 10.2140/agt.2011.11.2829
(4) Algebraic & Geometric Topology 11 (2011) 28612901 On the derivation algebra of the free Lie algebra and trace maps by Naoya Enomoto and Takao Satoh URL: http://www.msp.warwick.ac.uk/agt/2011/1105/p092.xhtml DOI: 10.2140/agt.2011.11.2861
Five papers have been published by Geometry & Topology; papers (5)(8) complete Volume 15 Issue 3, paper (9) opens Issue 4:
(5) Geometry & Topology 15 (2011) 16171650 Homological Lagrangian monodromy by Shengda Hu, Franois Lalonde and Remi Leclercq URL: http://www.msp.warwick.ac.uk/gt/2011/1503/p041.xhtml DOI: 10.2140/gt.2011.15.1617
(6) Geometry & Topology 15 (2011) 16511706 The moduli space of stable quotients by Alina Marian, Dragos Oprea and Rahul Pandharipande URL: http://www.msp.warwick.ac.uk/gt/2011/1503/p042.xhtml DOI: 10.2140/gt.2011.15.1651
(7) Geometry & Topology 15 (2011) 17071747 Parallelogram decompositions and generic surfaces in H^hyp(4) by DucManh Nguyen URL: http://www.msp.warwick.ac.uk/gt/2011/1503/p043.xhtml DOI: 10.2140/gt.2011.15.1707
(8) Geometry & Topology 15 (2011) 17491842 Sutures and contact homology I by Vincent Colin, Paolo Ghiggini, Ko Honda and Michael Hutchings URL: http://www.msp.warwick.ac.uk/gt/2011/1503/p044.xhtml DOI: 10.2140/gt.2011.15.1749
(9) Geometry & Topology 15 (2011) 18431882 On exceptional quotient singularities by Ivan Cheltsov and Constantin Shramov URL: http://www.msp.warwick.ac.uk/gt/2011/1504/p045.xhtml DOI: 10.2140/gt.2011.15.1843
Abstracts follow
(1) Deltadiscrete Gspectra and iterated homotopy fixed points by Daniel G Davis
Let G be a profinite group with finite virtual cohomological dimension and let X be a discrete Gspectrum. If H and K are closed subgroups of G, with H normal in K, then, in general, the K/Hspectrum X^{hH} is not known to be a continuous K/Hspectrum, so that it is not known (in general) how to define the iterated homotopy fixed point spectrum (X^{hH})^{hK/H}. To address this situation, we define homotopy fixed points for deltadiscrete Gspectra and show that the setting of deltadiscrete Gspectra gives a good framework within which to work. In particular, we show that by using deltadiscrete K/Hspectra, there is always an iterated homotopy fixed point spectrum, denoted (X^{hH})^{h_delta K/H}, and it is just X^{hK}.
Additionally, we show that for any deltadiscrete Gspectrum Y, there is an equivalence (Y^{h_delta H})^{h_delta K/H} ~= Y^{h_delta K}. Furthermore, if G is an arbitrary profinite group, there is a deltadiscrete Gspectrum X_delta that is equivalent to X and, though X^{hH} is not even known in general to have a K/Haction, there is always an equivalence ((X_\delta)^{h_delta H})^{h_delta K/H} ~= (X_delta)^{h_delta K}. Therefore, deltadiscrete Lspectra, by letting L equal H, K and K/H, give a way of resolving undesired deficiencies in our understanding of homotopy fixed points for discrete Gspectra.
(2) A loop theorem/Dehn's lemma for some orbifolds by Josh Barnard
The equivariant loop theorem implies the existence of a loop theorem/Dehn's lemma for 3orbifolds that are good (covered by a 3manifold). In this note we prove a loop theorem/Dehn's lemma for any locally orientable 3orbifold (good or bad) whose singular set is labeled with powers of 2. The proof is modeled on the standard tower construction.
(3) Spectral sequences in string topology by Lennart Meier
In this paper, we investigate the behavior of the Serre spectral sequence with respect to the algebraic structures of string topology in generalized homology theories, specifically with the ChasSullivan product and the corresponding coproduct and module structures. We prove compatibility for two kinds of fiber bundles: the fiber bundle Omega^n M > L^n M > M for an h_*oriented manifold M and the looped fiber bundle L^n F > L^n E > L^n B of a fiber bundle F > E > B of h_*oriented manifolds. Our method lies in the construction of Gysin morphisms of spectral sequences. We apply these results to study the ordinary homology of the free loop spaces of sphere bundles and some generalized homologies of the free loop spaces of spheres and projective spaces. For the latter purpose, we construct explicit manifold generators for the homology of these spaces.
(4) On the derivation algebra of the free Lie algebra and trace maps by Naoya Enomoto and Takao Satoh
We mainly study the derivation algebra of the free Lie algebra and the Chen Lie algebra generated by the abelianization H of a free group, and trace maps. To begin with, we give the irreducible decomposition of the derivation algebra as a GL(n,Q)module via the SchurWeyl duality and some tensor product theorems for GL(n,Q). Using them, we calculate the irreducible decomposition of the images of the Johnson homomorphisms of the automorphism group of a free group and a free metabelian group.
Next, we consider some applications of trace maps: Morita's trace map and the trace map for the exterior product of H. First, we determine the abelianization of the derivation algebra of the Chen Lie algebra as a Lie algebra, and show that the abelianization is given by the degree one part and Morita's trace maps. Second, we consider twisted cohomology groups of the automorphism group of a free nilpotent group. In particular, we show that the trace map for the exterior product of H defines a nontrivial twisted second cohomology class of it.
(5) Homological Lagrangian monodromy by Shengda Hu, Francois Lalonde and Remi Leclercq
We show that the Hamiltonian Lagrangian monodromy group, in its homological version, is trivial for any weakly exact Lagrangian submanifold of a symplectic manifold. The proof relies on a sheaf approach to Floer homology given by a relative Seidel morphism.
(6) The moduli space of stable quotients by Alina Marian, Dragos Oprea and Rahul Pandharipande
A moduli space of stable quotients of the rank n trivial sheaf on stable curves is introduced. Over nonsingular curves, the moduli space is Grothendieck's Quot scheme. Over nodal curves, a relative construction is made to keep the torsion of the quotient away from the singularities. New compactifications of classical spaces arise naturally: a nonsingular and irreducible compactification of the moduli of maps from genus 1 curves to projective space is obtained. Localization on the moduli of stable quotients leads to new relations in the tautological ring generalizing BrillNoether constructions.
The moduli space of stable quotients is proven to carry a canonical 2term obstruction theory and thus a virtual class. The resulting system of descendent invariants is proven to equal the GromovWitten theory of the Grassmannian in all genera. Stable quotients can also be used to study CalabiYau geometries. The conifold is calculated to agree with stable maps. Several questions about the behavior of stable quotients for arbitrary targets are raised.
(7) Parallelogram decompositions and generic surfaces in H^hyp(4) by DucManh Nguyen
The space H^hyp(4) is the moduli space of pairs (M,omega), where M is a hyperelliptic Riemann surface of genus 3 and omega is a holomorphic 1form having only one zero. In this paper, we first show that every surface in H^hyp(4) admits a decomposition into parallelograms and simple cylinders following a unique model. We then show that if this decomposition satisfies some irrational condition, then the GL^+(2,R)orbit of the surface is dense in H^hyp(4); such surfaces are called generic. Using this criterion, we prove that there are generic surfaces in H^hyp(4) with coordinates in any quadratic field, and there are ThurstonVeech surfaces with trace field of degree three over Q which are generic.
(8) Sutures and contact homology I by Vincent Colin, Paolo Ghiggini, Ko Honda and Michael Hutchings
We define a relative version of contact homology for contact manifolds with convex boundary and prove basic properties of this relative contact homology. Similar considerations also hold for embedded contact homology.
(9) On exceptional quotient singularities by Ivan Cheltsov and Constantin Shramov
We study exceptional quotient singularities. In particular, we prove an exceptionality criterion in terms of the alphainvariant of Tian, and utilize it to classify fourdimensional and fivedimensional exceptional quotient singularities.
Geometry & Topology Publications is an imprint of Mathematical Sciences Publishers.



