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Geometry and Topology

Posts: 140
Registered: 5/24/06
Nine papers published by Geometry & Topology Publications
Posted: Oct 15, 2011 9:35 AM
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Four papers have been published by Algebraic & Geometric Topology:

(1) Algebraic & Geometric Topology 11 (2011) 2775-2814
   Delta-discrete G-spectra and iterated homotopy fixed points
     by Daniel G Davis
   URL: http://www.msp.warwick.ac.uk/agt/2011/11-05/p089.xhtml
   DOI: 10.2140/agt.2011.11.2775

(2) Algebraic & Geometric Topology 11 (2011) 2815-2827
   A loop theorem/Dehn's lemma for some orbifolds
     by Josh Barnard
   URL: http://www.msp.warwick.ac.uk/agt/2011/11-05/p090.xhtml
   DOI: 10.2140/agt.2011.11.2815

(3) Algebraic & Geometric Topology 11 (2011) 2829-2860
   Spectral sequences in string topology
     by Lennart Meier
   URL: http://www.msp.warwick.ac.uk/agt/2011/11-05/p091.xhtml
   DOI: 10.2140/agt.2011.11.2829

(4) Algebraic & Geometric Topology 11 (2011) 2861-2901
   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/2011/11-05/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) 1617-1650
   Homological Lagrangian monodromy
     by Shengda Hu, Franois Lalonde and Remi Leclercq
   URL: http://www.msp.warwick.ac.uk/gt/2011/15-03/p041.xhtml
   DOI: 10.2140/gt.2011.15.1617

(6) Geometry & Topology 15 (2011) 1651-1706
   The moduli space of stable quotients
     by Alina Marian, Dragos Oprea and Rahul Pandharipande
   URL: http://www.msp.warwick.ac.uk/gt/2011/15-03/p042.xhtml
   DOI: 10.2140/gt.2011.15.1651

(7) Geometry & Topology 15 (2011) 1707-1747
   Parallelogram decompositions and generic surfaces in H^hyp(4)
     by Duc-Manh Nguyen
   URL: http://www.msp.warwick.ac.uk/gt/2011/15-03/p043.xhtml
   DOI: 10.2140/gt.2011.15.1707

(8) Geometry & Topology 15 (2011) 1749-1842
   Sutures and contact homology I
     by Vincent Colin, Paolo Ghiggini, Ko Honda and Michael Hutchings
   URL: http://www.msp.warwick.ac.uk/gt/2011/15-03/p044.xhtml
   DOI: 10.2140/gt.2011.15.1749

(9) Geometry & Topology 15 (2011) 1843-1882
   On exceptional quotient singularities
     by Ivan Cheltsov and Constantin Shramov
   URL: http://www.msp.warwick.ac.uk/gt/2011/15-04/p045.xhtml
   DOI: 10.2140/gt.2011.15.1843

Abstracts follow

(1) Delta-discrete G-spectra 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 G-spectrum. If H and K are closed subgroups of
G, with H normal in K, then, in general, the K/H-spectrum X^{hH} is
not known to be a continuous K/H-spectrum, 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 delta-discrete G-spectra and show that the setting of
delta-discrete G-spectra gives a good framework within which to work.
In particular, we show that by using delta-discrete K/H-spectra, 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 delta-discrete G-spectrum 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
delta-discrete G-spectrum X_delta that is equivalent to X and, though
X^{hH} is not even known in general to have a K/H-action, there is
always an equivalence ((X_\delta)^{h_delta H})^{h_delta K/H} ~=
(X_delta)^{h_delta K}. Therefore, delta-discrete L-spectra, 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 G-spectra.


(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 3-orbifolds that are good (covered by a
3-manifold). In this note we prove a loop theorem/Dehn's lemma for any
locally orientable 3-orbifold (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 Chas-Sullivan
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 Schur-Weyl
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 Brill-Noether constructions.

The moduli space of stable quotients is proven to carry a canonical
2-term obstruction theory and thus a virtual class.  The resulting
system of descendent invariants is proven to equal the Gromov-Witten
theory of the Grassmannian in all genera. Stable quotients can also be
used to study Calabi-Yau 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 Duc-Manh 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
1-form 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 Thurston-Veech 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 alpha-invariant of Tian,
and utilize it to classify four-dimensional and five-dimensional
exceptional quotient singularities.



  Geometry & Topology Publications is an imprint of
  Mathematical Sciences Publishers.



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