Twelve papers published by Geometry & Topology Publications

[Geometry and Topology]

even papers have been published by Algebraic & Geometric Topology:
Paper (1) completes Issue 3 of Volume 13 and (2)-(7) open Issue 4

(1) Algebraic & Geometric Topology 13 (2013) 1815-1856
   Dehn surgery, rational open books and knot Floer homology
     by Matthew Hedden and Olga Plamenevskaya
   URL: http://www.msp.warwick.ac.uk/agt/2013/13-03/p058.xhtml
   DOI: 10.2140/agt.2013.13.1815

(2) Algebraic & Geometric Topology 13 (2013) 1857-1935
   Diagram spaces, diagram spectra and spectra of units
     by John A Lind
   URL: http://www.msp.warwick.ac.uk/agt/2013/13-04/p059.xhtml
   DOI: 10.2140/agt.2013.13.1857

(3) Algebraic & Geometric Topology 13 (2013) 1937-1965
   Non-left-orderable double branched coverings
     by Tetsuya Ito
   URL: http://www.msp.warwick.ac.uk/agt/2013/13-04/p060.xhtml
   DOI: 10.2140/agt.2013.13.1937

(4) Algebraic & Geometric Topology 13 (2013) 1967-2000
   Simplicial presheaves of coalgebras
     by George Raptis
   URL: http://www.msp.warwick.ac.uk/agt/2013/13-04/p061.xhtml
   DOI: 10.2140/agt.2013.13.1967

(5) Algebraic & Geometric Topology 13 (2013) 2001-2037
   Closed surfaces and character varieties
     by Eric Chesebro
   URL: http://www.msp.warwick.ac.uk/agt/2013/13-04/p062.xhtml
   DOI: 10.2140/agt.2013.13.2001

(6) Algebraic & Geometric Topology 13 (2013) 2039-2060
   On the spectral sequence of the Swiss-cheese operad
     by Eduardo Hoefel and Muriel Livernet
   URL: http://www.msp.warwick.ac.uk/agt/2013/13-04/p063.xhtml
   DOI: 10.2140/agt.2013.13.2039

(7) Algebraic & Geometric Topology 13 (2013) 2061-2085
   The hit problem for H^*(BU(2);F_p)
     by David Pengelley and Frank Williams
   URL: http://www.msp.warwick.ac.uk/agt/2013/13-04/p064.xhtml
   DOI: 10.2140/agt.2013.13.2061

Three papers have been published by Geometry & Topology completing
Issue 2 of Volume 17

(8) Geometry & Topology 17 (2013) 1199-1203
   Addendum to "Commensurations and subgroups  
   of finite index of Thompson's group F"
     by Jose Burillo, Sean Cleary and Claas E Roever
   URL: http://www.msp.warwick.ac.uk/gt/2013/17-02/p027.xhtml
   DOI: 10.2140/gt.2013.17.1199

(9) Geometry & Topology 17 (2013) 1205-1223
   Continuous families of divisors, paracanonical systems and a
   new inequality for varieties of maximal Albanese dimension
     by Margarida Mendes Lopes, Rita Pardini and Gian Pietro Pirola
   URL: http://www.msp.warwick.ac.uk/gt/2013/17-02/p028.xhtml
   DOI: 10.2140/gt.2013.17.1205

(10) Geometry & Topology 17 (2013) 1225-1252
   Contact Anosov flows on hyperbolic 3-manifolds
     by Patrick Foulon and Boris Hasselblatt
   URL: http://www.msp.warwick.ac.uk/gt/2013/17-02/p029.xhtml
   DOI: 10.2140/gt.2013.17.1225

Two papers have been published by Geometry & Topology Monographs
as part of Volume 18, the FreedmanFest

(11) Geometry & Topology Monographs 18 (2012) 309-367
   Homological algebra of knots and BPS states
     by Sergei Gukov and Marko Stosic
   URL: http://www.msp.warwick.ac.uk/gtm/2012/18/p015.xhtml
   DOI: 10.2140/gtm.2012.18.309

(12) Geometry & Topology Monographs 18 (2012) 369-450
   Smooth structures on Morse trajectory spaces,  
   featuring finite ends and associative gluing
     by Katrin Wehrheim
   URL: http://www.msp.warwick.ac.uk/gtm/2012/18/p016.xhtml
   DOI: 10.2140/gtm.2012.18.369

Abstracts follow

(1) Dehn surgery, rational open books and knot Floer homology
     by Matthew Hedden and Olga Plamenevskaya

By recent results of Baker, Etnyre and Van Horn-Morris, a rational
open book decomposition defines a compatible contact structure.  We
show that the Heegaard Floer contact invariant of such a contact
structure can be computed in terms of the knot Floer homology of its
(rationally null-homologous) binding.  We then use this description of
contact invariants, together with a formula for the knot Floer
homology of the core of a surgery solid torus, to show that certain
manifolds obtained by surgeries on bindings of open books carry tight
contact structures.


(2) Diagram spaces, diagram spectra  and spectra of units
     by John A Lind

This article compares the infinite loop spaces associated to symmetric
spectra, orthogonal spectra and EKMM S-modules.  Each of these
categories of structured spectra has a corresponding category of
structured spaces that receives the infinite loop space functor
Omega^\infty.  We prove that these models for spaces are Quillen
equivalent and that the infinite loop space functors Omega^\infty
agree.  This comparison is then used to show that two different
constructions of the spectrum of units gl_1 R of a commutative ring
spectrum R agree.


(3) Non-left-orderable double branched coverings
     by Tetsuya Ito

We develop a method to show the fundamental group of the double
branched covering of links is not left-orderable by introducing a
notion of coarse presentation. Like usual group presentations, a
coarse presentation is given by a set of generators and relations, but
inequalities are allowed as relations. By using coarse presentations,
we give a family of links whose double branched covering has
non-left-orderable fundamental group. Our family of links includes
many known and new examples.


(4) Simplicial presheaves of coalgebras
     by George Raptis

The category of simplicial R-coalgebras over a presheaf of commutative
unital rings on a small Grothendieck site is endowed with a left
proper, simplicial, cofibrantly generated model category structure
where the weak equivalences are the local weak equivalences of the
underlying simplicial presheaves. This model category is naturally
linked to the R-local homotopy theory of simplicial presheaves and the
homotopy theory of simplicial R-modules by Quillen adjunctions. We
study the comparison with the R-local homotopy theory of simplicial
presheaves in the special case where R is a presheaf of algebraically
closed (or perfect) fields. If R is a presheaf of algebraically closed
fields, we show that the R-local homotopy category of simplicial
presheaves embeds fully faithfully in the homotopy category of
simplicial R-coalgebras.


(5) Closed surfaces and character varieties
     by Eric Chesebro

The powerful character variety techniques of Culler and Shalen can be
used to find essential surfaces in knot manifolds.  We show that module
structures on the coordinate ring of the character variety can be used
to identify detected boundary slopes as well as when closed surfaces
are detected.   This approach also yields new number theoretic
invariants
for the character varieties of knot manifolds.


(6) On the spectral sequence of the Swiss-cheese operad
     by Eduardo Hoefel and Muriel Livernet

We prove that the homology of the Swiss-cheese operad is a Koszul
operad. As a consequence, we obtain that the spectral sequence
associated to the stratification of the compactification of points on
the upper half plane collapses at the second stage, proving a
conjecture by A Voronov [Contemp. Math. 239 (1999) 365-373]. However,
we prove that the operad obtained at the second stage differs from the
homology of the Swiss-cheese operad.


(7) The hit problem for H^*(BU(2);F_p)
     by David Pengelley and Frank Williams

The hit problem for a module over the Steenrod algebra A seeks a
minimal set of A-generators ("non-hit elements"). This problem has
been studied for 25 years in a variety of contexts, and although
complete results have been notoriously difficult to come by, partial
results have been obtained in many cases.
For the cohomologies of classifying spaces, several such results
possess two intriguing features: sparseness by degree, and uniform
rank bounds independent of degree. In particular, it is known that
sparseness holds for H^*(BO(n);F_2) for all n, and that there is a
rank bound for n at most 3. Our results in this paper show that both
these features continue at all odd primes for BU(n) for n at most 2.
We solve the odd primary hit problem for H^*(BU(2);F_p) by determining
an explicit basis for the A-primitives in the dual H_*(BU(2);F_p),
where we find considerably more elaborate structure than in the
2-primary case. We obtain our results by structuring the
A-primitives in homology using an action of the Kudo-Araki-May
algebra.  

(8) Addendum to "Commensurations and subgroups  
   of finite index of Thompson's group F"
     by Jose Burillo, Sean Cleary and Claas E Roever

We show that the abstract commensurator of F is composed of four
building blocks: two isomorphism types of simple groups, the
multiplicative group of the positive rationals and a cyclic group of
order two.  The main result establishes the simplicity of a certain
group of piecewise linear homeomorphisms of the real line.


(9) Continuous families of divisors, paracanonical systems and
   a new inequality for varieties of maximal Albanese dimension
     by Margarida Mendes Lopes, Rita Pardini and Gian Pietro Pirola

Given a smooth complex projective variety X, a line bundle L of X and
v in H^1(O_X), we say that v is k-transversal to L if the complex
H^{k-1}(L) --> H^k(L) --> H^{k+1}(L) is exact. We prove that if v is
1-transversal to L and s in H^0(L) satisfies s cup v=0, then the first
order deformation (s_v, L_v) of the pair (s,L) in the direction v
extends to an analytic deformation.
We apply this result to improve known results on the paracanonical
system of a variety of maximal Albanese dimension, due to Beauville in
the case of surfaces and to Lazarsfeld-Popa in higher dimension.  In
particular, we prove the inequality p_g(X) >= chi(K_X)+q(X)-1 for a
variety X of maximal Albanese dimension without irregular fibrations
of Albanese general type.


(10) Contact Anosov flows on hyperbolic 3-manifolds
     by Patrick Foulon and Boris Hasselblatt

Geodesic flows of Riemannian or Finsler manifolds have been the only
known contact Anosov flows. We show that even in dimension 3 the world
of contact Anosov flows is vastly larger via a surgery construction
near an E-transverse Legendrian link that encompasses both the
Handel-Thurston and Goodman surgeries and that produces flows not
topologically orbit equivalent to any algebraic flow. This includes
examples on many hyperbolic 3-manifolds, any of which have remarkable
dynamical and geometric properties.
To the latter end we include a proof of a folklore theorem from
3-manifold topology: In the unit tangent bundle of a hyperbolic
surface, the complement of a knot that projects to a filling geodesic
is a hyperbolic 3-manifold.


(11) Homological algebra of knots and BPS states
     by Sergei Gukov and Marko Stosic

It is known that knot homologies admit a physical description as
spaces of open BPS states.  We study operators and algebras acting on
these spaces.  This leads to a very rich story, which involves
wall-crossing phenomena, algebras of closed BPS states acting on
spaces of open BPS states and deformations of Landau-Ginzburg models.
An important application to knot homologies is the existence of
"colored differentials" that relate homological invariants of knots
colored by different representations.  Based on this structure, we
formulate a list of properties of the colored HOMFLY homology that
categorifies the colored HOMFLY polynomial.  By calculating the
colored HOMFLY homology for symmetric and antisymmetric
representations, we find a remarkable "mirror symmetry" between these
triply graded theories.


(12) Smooth structures on Morse trajectory spaces,  
    featuring finite ends and associative gluing
     by Katrin Wehrheim

We give elementary constructions of manifold with corner structures
and associative gluing maps on compactifications of spaces of
infinite, half infinite and finite Morse flow lines.  In the case of
Euclidean metric in Morse coordinates near each critical point, these
are naturally given by evaluations at end points and regular level
sets. For finite ends this requires a blowup construction near
trajectories ending at critical points.



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