Jump to ContentJump to Main Navigation

Forum Mathematicum

Managing Editor: Brüdern, Jörg

Editorial Board Member: Bruinier, Jan Hendrik / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Gallavotti, Giovanni / Garnier, Josselin / Neeb, Karl-Hermann / Noguchi, Junjiro / Ranicki, Andrew / Segal, Dan / Shahidi, Freydoon / Shigekawa, Ichiro / Sogge, Christopher D. / Strambach, Karl

6 Issues per year

IMPACT FACTOR 2012: 0.527
5-year IMPACT FACTOR: 0.718
Mathematical Citation Quotient 2012: 0.68

VolumeIssuePage

Issues

Characteristic cohomotopy classes for families of 4-manifolds

Markus Szymik1

1Fakultät für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, Germany.

Citation Information: Forum Mathematicum. Volume 22, Issue 3, Pages 509–523, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: 10.1515/forum.2010.027, February 2010

Publication History:
Received:
2007-09-12
Accepted:
2008-08-06
Published Online:
2010-02-08

Abstract

Families of smooth closed oriented 4-manifolds with a complex spin structure are studied by means of a family version of the Bauer-Furuta invariants. The definition is given in the context of parametrised stable homotopy theory, but an interpretation in terms of characteristic cohomotopy classes on Thom spectra associated to the classifying spaces of complex spin diffeomorphism groups is given as well. The theory is illustrated with families of K3 surfaces and mapping tori of diffeomorphisms. It is also related to equivariant invariants.

Comments (0)

Please log in or register to comment.
Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.