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Nine papers published by Geometry & Topology Publications
Posted:
May 10, 2011 8:55 PM


Six papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 11 (2011) 11071162 Differential operators and the wheels power series by Andrew Kricker URL: http://www.msp.warwick.ac.uk/agt/2011/1102/p036.xhtml DOI: 10.2140/agt.2011.11.1107
(2) Algebraic & Geometric Topology 11 (2011) 11631203 Homotopy algebra structures on twisted tensor products and string topology operations by Micah Miller URL: http://www.msp.warwick.ac.uk/agt/2011/1102/p037.xhtml DOI: 10.2140/agt.2011.11.1163
(3) Algebraic & Geometric Topology 11 (2011) 12051242 Meridional destabilizing number of knots by Toshio Saito URL: http://www.msp.warwick.ac.uk/agt/2011/1102/p038.xhtml DOI: 10.2140/agt.2011.11.1205
(4) Algebraic & Geometric Topology 11 (2011) 12431256 Knots which admit a surgery with simple knot Floer homology groups by Eaman Eftekhary URL: http://www.msp.warwick.ac.uk/agt/2011/1103/p039.xhtml DOI: 10.2140/agt.2011.11.1243
(5) Algebraic & Geometric Topology 11 (2011) 12571265 Coverings and minimal triangulations of 3manifolds by William Jaco, J Hyam Rubinstein and Stephan Tillmann URL: http://www.msp.warwick.ac.uk/agt/2011/1103/p040.xhtml DOI: 10.2140/agt.2011.11.1257
(6) Algebraic & Geometric Topology 11 (2011) 12671322 On genus1 simplified broken Lefschetz fibrations by Kenta Hayano URL: http://www.msp.warwick.ac.uk/agt/2011/1103/p041.xhtml DOI: 10.2140/agt.2011.11.1267
Three papers have been published by Geometry & Topology
(7) Geometry & Topology 15 (2011) 609676 Central extensions of smooth 2groups and a finitedimensional string 2group by Christopher J SchommerPries URL: http://www.msp.warwick.ac.uk/gt/2011/1502/p017.xhtml DOI: 10.2140/gt.2011.15.609
(8) Geometry & Topology 15 (2011) 677697 On GromovHausdorff stability in a boundary rigidity problem by Sergei Ivanov URL: http://www.msp.warwick.ac.uk/gt/2011/1502/p018.xhtml DOI: 10.2140/gt.2011.15.677
(9) Geometry & Topology 15 (2011) 699705 Directed immersions of closed manifolds by Mohammad Ghomi URL: http://www.msp.warwick.ac.uk/gt/2011/1502/p019.xhtml DOI: 10.2140/gt.2011.15.699
Abstracts follow
(1) Differential operators and the wheels power series by Andrew Kricker
An earlier work of the author's showed that it was possible to adapt the AlekseevMeinrenken ChernWeil proof of the Duflo isomorphism to obtain a completely combinatorial proof of the wheeling isomorphism. That work depended on a certain combinatorial identity, which said that a particular composition of elementary combinatorial operations arising from the proof was precisely the wheeling operation. The identity can be summarized as follows: The wheeling operation is just a graded averaging map in a space enlarging the space of Jacobi diagrams. The purpose of this paper is to present a detailed and selfcontained proof of this identity. The proof broadly follows similar calculations in the AlekseevMeinrenken theory, though the details here are somewhat different, as the algebraic manipulations in the original are replaced with arguments concerning the enumerative combinatorics of formal power series of graphs with graded legs.
(2) Homotopy algebra structures on twisted tensor products and string topology operations by Micah Miller
Given a Cinfinity coalgebra C_*, a strict dg Hopf algebra H_* and a twisting cochain tau: C_* > H_* such that Im(tau) is in Prim(H_*), we describe a procedure for obtaining an Ainfinity coalgebra on the tensor product of C_* with H_*. This is an extension of Brown's work on twisted tensor products. We apply this procedure to obtain an Ainfinity coalgebra model of the chains on the free loop space LM based on the Cinfinity coalgebra structure of H_*(M) induced by the diagonal map M > M x M and the Hopf algebra model of the based loop space given by T(H_*(M)[1]). When C_* has cyclic Cinfinity coalgebra structure, we describe an Ainfinity algebra on the tensor product of C_* with H_*. This is used to give an explicit (nonminimal) Ainfinity algebra model of the string topology loop product. Finally, we discuss a representation of the loop product in principal Gbundles.
(3) Meridional destabilizing number of knots by Toshio Saito
We define the meridional destabilizing number of a knot. This together with Heegaard genus (or tunnel number) gives a binary complexity of knots. We study its behavior under connected sum of tunnel number one knots.
(4) Knots which admit a surgery with simple knot Floer homology groups by Eaman Eftekhary
We show that if a positive integral surgery on a knot K inside a homology sphere X results in an induced knot K_n in X_n(K)=Y which has simple Floer homology then n >= 2g(K). Moreover, for X=S^3 the threemanifold Y is an Lspace, and the Heegaard Floer homology groups of K are determined by its Alexander polynomial.
(5) Coverings and minimal triangulations of 3manifolds by William Jaco, J Hyam Rubinstein and Stephan Tillmann
This paper uses results on the classification of minimal triangulations of 3manifolds to produce additional results, using covering spaces. Using previous work on minimal triangulations of lens spaces, it is shown that the lens space L(4k,2k1) and the generalised quaternionic space which is the quotient of the threesphere by Q_4k have complexity k, where k is at least 2. Moreover, it is shown that their minimal triangulations are unique.
(6) On genus1 simplified broken Lefschetz fibrations by Kenta Hayano
Auroux, Donaldson and Katzarkov introduced broken Lefschetz fibrations as a generalization of Lefschetz fibrations in order to describe nearsymplectic 4manifolds. We first study monodromy representations of higher sides of genus1 simplified broken Lefschetz fibrations. We then completely classify diffeomorphism types of such fibrations with connected fibers and with less than six Lefschetz singularities. In these studies, we obtain several families of genus1 simplified broken Lefschetz fibrations, which we conjecture contain all such fibrations, and determine the diffeomorphism types of the total spaces of these fibrations. Our results are generalizations of Kas' classification theorem of genus1 Lefschetz fibrations, which states that the total space of a nontrivial genus1 Lefschetz fibration over the 2sphere is diffeomorphic to an elliptic surface E(n) for some n at least 1.
(7) Central extensions of smooth 2groups and a finitedimensional string 2group by Christopher J SchommerPries
We provide a model of the String group as a central extension of finitedimensional 2groups in the bicategory of Lie groupoids, leftprincipal bibundles, and bibundle maps. This bicategory is a geometric incarnation of the bicategory of smooth stacks and generalizes the more naive 2category of Lie groupoids, smooth functors and smooth natural transformations. In particular this notion of smooth 2group subsumes the notion of Lie 2group introduced by Baez and Lauda [Theory Appl. Categ. 12 (2004) 423491]. More precisely we classify a large family of these central extensions in terms of the topological group cohomology introduced by Segal [Symposia Mathematica, Vol. IV (INDAM, Rome, 1968/69), Academic Press, London (1970) 377387], and our String 2group is a special case of such extensions. There is a nerve construction which can be applied to these 2groups to obtain a simplicial manifold, allowing comparison with the model of Henriques [arXiv:math/0603563]. The geometric realization is an Ainfinityspace, and in the case of our model, has the correct homotopy type of String(n). Unlike all previous models, our construction takes place entirely within the framework of finitedimensional manifolds and Lie groupoids. Moreover within this context our model is characterized by a strong uniqueness result. It is a canonical central extension of Spin(n).
(8) On GromovHausdorff stability in a boundary rigidity problem by Sergei Ivanov
Let M be a compact Riemannian manifold with boundary. We show that M is GromovHausdorff close to a convex Euclidean region D of the same dimension if the boundary distance function of M is C^1close to that of D. More generally, we prove the same result under the assumptions that the boundary distance function of M is C^0close to that of D, the volumes of M and D are almost equal, and volumes of metric balls in M have a certain lower bound in terms of radius.
(9) Directed immersions of closed manifolds by Mohammad Ghomi
Given any finite subset X of the nsphere, n at least 2, which includes no pairs of antipodal points, we explicitly construct smoothly immersed closed orientable hypersurfaces in (n+1)dimensional Euclidean space whose Gauss map misses X. In particular, this answers a question of M Gromov.
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