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Five papers published by Geometry & Topology Publications
Posted:
Feb 15, 2012 9:01 PM
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Four papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 12 (2012) 49-74
Unstable Adams operations on p-local compact groups
by Fabien Junod, Ran Levi and Assaf Libman
URL: http://www.msp.warwick.ac.uk/agt/2012/12-01/p004.xhtml
DOI: 10.2140/agt.2012.12.49
(2) Algebraic & Geometric Topology 12 (2012) 75-94
Estimating the higher symmetric topological complexity of spheres
by Roman Karasev and Peter Landweber
URL: http://www.msp.warwick.ac.uk/agt/2012/12-01/p005.xhtml
DOI: 10.2140/agt.2012.12.75
(3) Algebraic & Geometric Topology 12 (2012) 95-108
On piecewise linear cell decompositions
by Alexander Kirillov, Jr
URL: http://www.msp.warwick.ac.uk/agt/2012/12-01/p006.xhtml
DOI: 10.2140/agt.2012.12.95
(4) Algebraic & Geometric Topology 12 (2012) 109-130
On diffeomorphisms over nonorientable surfaces standardly embedded
in the 4-sphere
by Susumu Hirose
URL: http://www.msp.warwick.ac.uk/agt/2012/12-01/p007.xhtml
DOI: 10.2140/agt.2012.12.109
One paper has been published by Geometry & Topology
(5) Geometry & Topology 16 (2012) 301-389
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/2012/16-01/p006.xhtml
DOI: 10.2140/gt.2012.16.301
Abstracts follow
(1) Unstable Adams operations on p-local compact groups
by Fabien Junod, Ran Levi and Assaf Libman
A p-local compact group is an algebraic object modelled on the p-local
homotopy theory of classifying spaces of compact Lie groups and
p-compact 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 p-local compact groups
and show that such operations exist under rather mild conditions. More
precisely, we prove that for a given p-local compact group G and a
sufficiently large positive integer m, there exists an injective group
homomorphism from the group of p-adic 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_m-equivariantly to any m-tuple 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^{2n-1} -> 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 4-sphere
by Susumu Hirose
For a nonorientable closed surface standardly embedded in the
4-sphere, a diffeomorphism over this surface is extendable if and only
if this diffeomorphism preserves the Guillou-Marin 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) 415--434].
Geometry & Topology Publications is an imprint of
Mathematical Sciences Publishers
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