Seven papers have been published by Algebraic & Geometric Topology. Papers (1)-(4) complete issue 2 of Volume 12 and papers (5)-(7) open issue 3.
(1) Algebraic & Geometric Topology 12 (2012) 1165-1181 Simplicial volume of Q-rank one locally symmetric spaces covered by the product of R-rank one symmetric spaces by Sungwoon Kim and Inkang Kim URL: http://www.msp.warwick.ac.uk/agt/2012/12-02/p043.xhtml DOI: 10.2140/agt.2012.12.1165
(2) Algebraic & Geometric Topology 12 (2012) 1183-1210 Rational tangle surgery and Xer recombination on catenanes by Isabel K Darcy, Kai Ishihara, Ram K Medikonduri and Koya Shimokawa URL: http://www.msp.warwick.ac.uk/agt/2012/12-02/p044.xhtml DOI: 10.2140/agt.2012.12.1183
(5) Algebraic & Geometric Topology 12 (2012) 1265-1272 Computation-free presentation of the fundamental group of generic (p,q)-torus curves by Enrique Artal Bartolo, Jose Ignacio Cogolludo Agustin and Jorge Ortigas-Galindo URL: http://www.msp.warwick.ac.uk/agt/2012/12-03/p047.xhtml DOI: 10.2140/agt.2012.12.1265
(1) Simplicial volume of Q-rank one locally symmetric spaces covered by the product of R-rank one symmetric spaces by Sungwoon Kim and Inkang Kim
In this paper, we show that the simplicial volume of Q-rank one locally symmetric spaces covered by the product of Q-rank one symmetric spaces is strictly positive.
(2) Rational tangle surgery and Xer recombination on catenanes by Isabel K Darcy, Kai Ishihara, Ram K Medikonduri and Koya Shimokawa
The protein recombinase can change the knot type of circular DNA. The action of a recombinase converting one knot into another knot is normally mathematically modeled by band surgery. Band surgeries on a 2-bridge knot N((4mn-1)/2m) yielding a (2,2k)-torus link are characterized. We apply this and other rational tangle surgery results to analyze Xer recombination on DNA catenanes using the tangle model for protein-bound DNA.
(3) Homotopy normal maps by Matan Prezma
A group property made homotopical is a property of the corresponding classifying space. This train of thought can lead to a homotopical definition of normal maps between topological groups (or loop spaces).
In this paper we deal with such maps, called homotopy normal maps, which are topological group maps from N to G G being "normal" in that they induce a compatible topological group structure on the homotopy quotient G//N:=EN x_N G. We develop the notion of homotopy normality and its basic properties, and show it is invariant under homotopy monoidal endofunctors of topological spaces, eg localizations and completions. In the course of characterizing normality, we define a notion of a homotopy action of a loop space on a space phrased in terms of Segal's 1-fold delooping machine. Homotopy actions are "flexible" in the sense they are invariant under homotopy monoidal functors, but can also rigidify to (strict) group actions.
(4) On the augmentation quotients of the IA-automorphism group of a free group by Takao Satoh
We study the augmentation quotients of the IA-automorphism group of a free group and a free metabelian group. First, for any group G, we construct a lift of the k-th Johnson homomorphism of the automorphism group of G to the k-th augmentation quotient of the IA-automorphism group of G. Then we study the images of these homomorphisms for the case where G is a free group and a free metabelian group. As a corollary, we detect a Z-free part in each of the augmentation quotients, which can not be detected by the abelianization of the IA-automorphism group.
(5) Computation-free presentation of the fundamental group of generic (p,q)-torus curves by Enrique Artal Bartolo, Jose Ignacio Cogolludo Agustin and Jorge Ortigas-Galindo
We present a new method for computing fundamental groups of curve complements using a variation of the Zariski-van Kampen method on general ruled surfaces. As an application we give an alternative (computation-free) proof for the fundamental group of generic (p,q)-torus curves.
(6) On Legendrian graphs by Danielle O'Donnol and Elena Pavelescu
We investigate Legendrian graphs in (R^3, xi_std). We extend the Thurston--Bennequin number and the rotation number to Legendrian graphs. We prove that a graph can be Legendrian realized with all its cycles Legendrian unknots with tb=-1 and rot=0 if and only if it does not contain K_4 as a minor. We show that the pair (tb, rot) does not characterize a Legendrian graph up to Legendrian isotopy if the graph contains a cut edge or a cut vertex. When we restrict to planar spatial graphs, a pair (tb, rot) determines two Legendrian isotopy classes of the lollipop graph and a pair (tb, rot) determines four Legendrian isotopy classes of the handcuff graph.
(7) A Jorgensen-Thurston theorem for homomorphisms by Yi Liu
We provide a description of the structure of the set of homomorphisms from a finitely generated group to any torsion-free (3-dimensional) Kleinian group with uniformly bounded finite covolume. This is analogous to the Jorgensen-Thurston Theorem in hyperbolic geometry.
(8) Localization theorems in topological Hochschild homology and topological cyclic homology by Andrew J Blumberg and Michael A Mandell
We construct localization cofibration sequences for the topological Hochschild homology (THH) and topological cyclic homology (TC) of small spectral categories. Using a global construction of the THH and TC of a scheme in terms of the perfect complexes in a spectrally enriched version of the category of unbounded complexes, the sequences specialize to localization cofibration sequences associated to the inclusion of an open subscheme. These are the targets of the cyclotomic trace from the localization sequence of Thomason-Trobaugh in K-theory. We also deduce versions of Thomason's blow-up formula and the projective bundle formula for THH and TC.
(9) Lagrangian spheres, symplectic surfaces and the symplectic mapping class group by Tian-Jun Li and Weiwei Wu
Given a Lagrangian sphere in a symplectic 4-manifold (M,omega) with b^+=1, we find embedded symplectic surfaces intersecting it minimally. When the Kodaira dimension kappa of (M,omega) is -infty, this minimal intersection property turns out to be very powerful for both the uniqueness and existence problems of Lagrangian spheres. On the uniqueness side, for a symplectic rational manifold and any class which is not characteristic, we show that homologous Lagrangian spheres are smoothly isotopic, and when the Euler number is less than 8, we generalize Hind and Evans' Hamiltonian uniqueness in the monotone case. On the existence side, when kappa=-infinity, we give a characterization of classes represented by Lagrangian spheres, which enables us to describe the non-Torelli part of the symplectic mapping class group.
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