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Twelve papers published by Geometry & Topology Publications
Posted:
May 30, 2013 8:04 AM


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) 18151856 Dehn surgery, rational open books and knot Floer homology by Matthew Hedden and Olga Plamenevskaya URL: http://www.msp.warwick.ac.uk/agt/2013/1303/p058.xhtml DOI: 10.2140/agt.2013.13.1815
(2) Algebraic & Geometric Topology 13 (2013) 18571935 Diagram spaces, diagram spectra and spectra of units by John A Lind URL: http://www.msp.warwick.ac.uk/agt/2013/1304/p059.xhtml DOI: 10.2140/agt.2013.13.1857
(3) Algebraic & Geometric Topology 13 (2013) 19371965 Nonleftorderable double branched coverings by Tetsuya Ito URL: http://www.msp.warwick.ac.uk/agt/2013/1304/p060.xhtml DOI: 10.2140/agt.2013.13.1937
(4) Algebraic & Geometric Topology 13 (2013) 19672000 Simplicial presheaves of coalgebras by George Raptis URL: http://www.msp.warwick.ac.uk/agt/2013/1304/p061.xhtml DOI: 10.2140/agt.2013.13.1967
(5) Algebraic & Geometric Topology 13 (2013) 20012037 Closed surfaces and character varieties by Eric Chesebro URL: http://www.msp.warwick.ac.uk/agt/2013/1304/p062.xhtml DOI: 10.2140/agt.2013.13.2001
(6) Algebraic & Geometric Topology 13 (2013) 20392060 On the spectral sequence of the Swisscheese operad by Eduardo Hoefel and Muriel Livernet URL: http://www.msp.warwick.ac.uk/agt/2013/1304/p063.xhtml DOI: 10.2140/agt.2013.13.2039
(7) Algebraic & Geometric Topology 13 (2013) 20612085 The hit problem for H^*(BU(2);F_p) by David Pengelley and Frank Williams URL: http://www.msp.warwick.ac.uk/agt/2013/1304/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) 11991203 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/2013/1702/p027.xhtml DOI: 10.2140/gt.2013.17.1199
(9) Geometry & Topology 17 (2013) 12051223 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/2013/1702/p028.xhtml DOI: 10.2140/gt.2013.17.1205
(10) Geometry & Topology 17 (2013) 12251252 Contact Anosov flows on hyperbolic 3manifolds by Patrick Foulon and Boris Hasselblatt URL: http://www.msp.warwick.ac.uk/gt/2013/1702/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) 309367 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) 369450 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 HornMorris, 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 nullhomologous) 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 Smodules. 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) Nonleftorderable double branched coverings by Tetsuya Ito
We develop a method to show the fundamental group of the double branched covering of links is not leftorderable 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 nonleftorderable fundamental group. Our family of links includes many known and new examples.
(4) Simplicial presheaves of coalgebras by George Raptis
The category of simplicial Rcoalgebras 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 Rlocal homotopy theory of simplicial presheaves and the homotopy theory of simplicial Rmodules by Quillen adjunctions. We study the comparison with the Rlocal 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 Rlocal homotopy category of simplicial presheaves embeds fully faithfully in the homotopy category of simplicial Rcoalgebras.
(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 Swisscheese operad by Eduardo Hoefel and Muriel Livernet
We prove that the homology of the Swisscheese 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) 365373]. However, we prove that the operad obtained at the second stage differs from the homology of the Swisscheese 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 Agenerators ("nonhit 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 Aprimitives in the dual H_*(BU(2);F_p), where we find considerably more elaborate structure than in the 2primary case. We obtain our results by structuring the Aprimitives in homology using an action of the KudoArakiMay 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 ktransversal to L if the complex H^{k1}(L) > H^k(L) > H^{k+1}(L) is exact. We prove that if v is 1transversal 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 LazarsfeldPopa 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 3manifolds 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 Etransverse Legendrian link that encompasses both the HandelThurston and Goodman surgeries and that produces flows not topologically orbit equivalent to any algebraic flow. This includes examples on many hyperbolic 3manifolds, any of which have remarkable dynamical and geometric properties. To the latter end we include a proof of a folklore theorem from 3manifold topology: In the unit tangent bundle of a hyperbolic surface, the complement of a knot that projects to a filling geodesic is a hyperbolic 3manifold.
(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 wallcrossing phenomena, algebras of closed BPS states acting on spaces of open BPS states and deformations of LandauGinzburg 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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