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Five papers published by Geometry & Topology Publications
Posted:
Feb 15, 2012 9:01 PM


Four papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 12 (2012) 4974 Unstable Adams operations on plocal compact groups by Fabien Junod, Ran Levi and Assaf Libman URL: http://www.msp.warwick.ac.uk/agt/2012/1201/p004.xhtml DOI: 10.2140/agt.2012.12.49
(2) Algebraic & Geometric Topology 12 (2012) 7594 Estimating the higher symmetric topological complexity of spheres by Roman Karasev and Peter Landweber URL: http://www.msp.warwick.ac.uk/agt/2012/1201/p005.xhtml DOI: 10.2140/agt.2012.12.75
(3) Algebraic & Geometric Topology 12 (2012) 95108 On piecewise linear cell decompositions by Alexander Kirillov, Jr URL: http://www.msp.warwick.ac.uk/agt/2012/1201/p006.xhtml DOI: 10.2140/agt.2012.12.95
(4) Algebraic & Geometric Topology 12 (2012) 109130 On diffeomorphisms over nonorientable surfaces standardly embedded in the 4sphere by Susumu Hirose URL: http://www.msp.warwick.ac.uk/agt/2012/1201/p007.xhtml DOI: 10.2140/agt.2012.12.109
One paper has been published by Geometry & Topology
(5) Geometry & Topology 16 (2012) 301389 Effect of Legendrian surgery by Frederic Bourgeois, Tobias Ekholm and Yasha Eliashberg Appendix: Sheel Ganatra and Maksim Maydanskiy URL: http://www.msp.warwick.ac.uk/gt/2012/1601/p006.xhtml DOI: 10.2140/gt.2012.16.301
Abstracts follow
(1) Unstable Adams operations on plocal compact groups by Fabien Junod, Ran Levi and Assaf Libman
A plocal compact group is an algebraic object modelled on the plocal homotopy theory of classifying spaces of compact Lie groups and pcompact groups. In the study of these objects unstable Adams operations are of fundamental importance. In this paper we define unstable Adams operations within the theory of plocal compact groups and show that such operations exist under rather mild conditions. More precisely, we prove that for a given plocal compact group G and a sufficiently large positive integer m, there exists an injective group homomorphism from the group of padic units which are congruent to 1 modulo p^m to the group of unstable Adams operations on G.
(2) Estimating the higher symmetric topological complexity of spheres by Roman Karasev and Peter Landweber
We study questions of the following type: Can one assign continuously and Sigma_mequivariantly to any mtuple of distinct points on the sphere S^n a multipath in S^n spanning these points? A multipath is a continuous map of the wedge of m segments to the sphere. This question is connected with the higher symmetric topological complexity of spheres, introduced and studied by I Basabe, J Gonzalez, Yu B Rudyak, and D Tamaki. In all cases we can handle, the answer is negative. Our arguments are in the spirit of the definition of the Hopf invariant of a map f: S^{2n1} > S^n by means of the mapping cone and the cup product.
(3) On piecewise linear cell decompositions by Alexander Kirillov, Jr
We introduce a class of cell decompositions of PL manifolds and polyhedra which are more general than triangulations yet not as general as CW complexes; we propose calling them PLCW complexes. The main result is an analog of Alexander's theorem: any two PLCW decompositions of the same polyhedron can be obtained from each other by a sequence of certain "elementary" moves.
This definition is motivated by the needs of Topological Quantum Field Theory, especially extended theories as defined by Lurie.
(4) On diffeomorphisms over nonorientable surfaces standardly embedded in the 4sphere by Susumu Hirose
For a nonorientable closed surface standardly embedded in the 4sphere, a diffeomorphism over this surface is extendable if and only if this diffeomorphism preserves the GuillouMarin quadratic form of this embedded surface.
(5) Effect of Legendrian surgery by Frederic Bourgeois, Tobias Ekholm and Yasha Eliashberg Appendix: Sheel Ganatra and Maksim Maydanskiy
The paper is a summary of the results of the authors concerning computations of symplectic invariants of Weinstein manifolds and contains some examples and applications. Proofs are sketched. The detailed proofs will appear in a forthcoming paper.
In the Appendix written by S Ganatra and M Maydanskiy it is shown that the results of this paper imply P Seidel's conjecture from [Proc. Sympos. Pure Math. 80, Amer. Math. Soc. (2009) 415434].
Geometry & Topology Publications is an imprint of Mathematical Sciences Publishers



