Volume 12, issue 1 (2012)

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ISSN (electronic): 1472-2739
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On diffeomorphisms over nonorientable surfaces standardly embedded in the $4$–sphere

Susumu Hirose

Algebraic & Geometric Topology 12 (2012) 109–130
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