#### Volume 12, issue 1 (2012)

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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