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

Susumu Hirose

doi:10.2140/agt.2012.12.109

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Home > Journals > Algebr. Geom. Topol. > Volume 12 > Issue 1 > Article

2012 On diffeomorphisms over nonorientable surfaces standardly embedded in the $4$–sphere

Susumu Hirose

Algebr. Geom. Topol. 12(1): 109-130 (2012). DOI: 10.2140/agt.2012.12.109

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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.

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Susumu Hirose. "On diffeomorphisms over nonorientable surfaces standardly embedded in the $4$–sphere." Algebr. Geom. Topol. 12 (1) 109 - 130, 2012. https://doi.org/10.2140/agt.2012.12.109

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Received: 11 September 2011; Revised: 24 October 2011; Accepted: 6 November 2011; Published: 2012

First available in Project Euclid: 19 December 2017

zbMATH: 1244.57043

MathSciNet: MR2889548

Digital Object Identifier: 10.2140/agt.2012.12.109

Subjects:

Primary: 57Q45

Secondary: 20F38 , 57N05

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

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Susumu Hirose "On diffeomorphisms over nonorientable surfaces standardly embedded in the $4$–sphere," Algebraic & Geometric Topology, Algebr. Geom. Topol. 12(1), 109-130, (2012)

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