Volume 2, issue 2 (2002)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
On diffeomorphisms over surfaces trivially embedded in the 4–sphere

Susumu Hirose

Algebraic & Geometric Topology 2 (2002) 791–824

arXiv: math.GT/0211019

Abstract

A surface in the 4–sphere is trivially embedded, if it bounds a 3–dimensional handle body in the 4–sphere. For a surface trivially embedded in the 4–sphere, a diffeomorphism over this surface is extensible if and only if this preserves the Rokhlin quadratic form of this embedded surface.

Keywords
knotted surface, mapping class group, spin mapping class group
Mathematical Subject Classification 2000
Primary: 57N10
Secondary: 57N05, 20F38
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Publication
Received: 6 March 2002
Accepted: 4 September 2002
Published: 3 October 2002
Authors
Susumu Hirose
Department of Mathematics
Faculty of Science and Engineering
Saga University
Saga
840-8502 Japan