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

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.

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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)

Susumu Hirose

Abstract