On diffeomorphisms over nonorientable surfaces standardly embedded in the 4–sphere

Hirose, Susumu

doi:10.2140/agt.2012.12.109

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On diffeomorphisms over nonorientable surfaces standardly embedded in the $4$–sphere

Susumu Hirose

Algebraic & Geometric Topology 12 (2012) 109–130

DOI: 10.2140/agt.2012.12.109

Abstract

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.

Keywords

mapping class group, nonorientable surface, knotted surface, Guillou–Marin quadratic form

Mathematical Subject Classification 2010

Primary: 57Q45

Secondary: 20F38, 57N05

References

Publication

Received: 11 September 2011

Revised: 24 October 2011

Accepted: 6 November 2011

Published: 15 February 2012

Authors

Susumu Hirose
Department of Mathematics Faculty of Science and Technology Tokyo University of Science Noda, Chiba 278-8510 Japan

Volume 12, issue 1 (2012)