Algebraic & Geometric Topology

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

Susumu Hirose

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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.

Article information

Source
Algebr. Geom. Topol., Volume 12, Number 1 (2012), 109-130.

Dates
Received: 11 September 2011
Revised: 24 October 2011
Accepted: 6 November 2011
First available in Project Euclid: 19 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715334

Digital Object Identifier
doi:10.2140/agt.2012.12.109

Mathematical Reviews number (MathSciNet)
MR2889548

Zentralblatt MATH identifier
1244.57043

Subjects
Primary: 57Q45: Knots and links (in high dimensions) {For the low-dimensional case, see 57M25}
Secondary: 20F38: Other groups related to topology or analysis 57N05: Topology of $E^2$ , 2-manifolds

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

Citation

Hirose, Susumu. On diffeomorphisms over nonorientable surfaces standardly embedded in the $4$–sphere. Algebr. Geom. Topol. 12 (2012), no. 1, 109--130. doi:10.2140/agt.2012.12.109. https://projecteuclid.org/euclid.agt/1513715334


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References

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