Surfaces in 4-manifolds and their mapping class groups

Susumu Hirose; Akira Yasuhara

doi:10.1016/j.top.2007.05.001

Surfaces in 4-manifolds and their mapping class groups

Susumu Hirose^*, Akira Yasuhara

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

A surface in a smooth 4-manifold is called flexible if, for any diffeomorphism φ{symbol} on the surface, there is a diffeomorphism on the 4-manifold whose restriction on the surface is φ{symbol} and which is isotopic to the identity. We investigate a sufficient condition for a smooth 4-manifold M to include flexible knotted surfaces, and introduce a local operation in simply connected 4-manifolds for obtaining a flexible knotted surface from any knotted surface.

Original language	English
Pages (from-to)	41-50
Number of pages	10
Journal	Topology
Volume	47
Issue number	1
DOIs	https://doi.org/10.1016/j.top.2007.05.001
Publication status	Published - 2008 Jan
Externally published	Yes

Keywords

4-dimensional manifold
Knotted surface
Mapping class group

ASJC Scopus subject areas

Geometry and Topology

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10.1016/j.top.2007.05.001

Cite this

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abstract = "A surface in a smooth 4-manifold is called flexible if, for any diffeomorphism φ{symbol} on the surface, there is a diffeomorphism on the 4-manifold whose restriction on the surface is φ{symbol} and which is isotopic to the identity. We investigate a sufficient condition for a smooth 4-manifold M to include flexible knotted surfaces, and introduce a local operation in simply connected 4-manifolds for obtaining a flexible knotted surface from any knotted surface.",

keywords = "4-dimensional manifold, Knotted surface, Mapping class group",

author = "Susumu Hirose and Akira Yasuhara",

note = "Funding Information: This research was partially supported by Grants-in-Aid for Encouragement of Young Scientists (No. 16740038 and No. 15740030), Ministry of Education, Culture, Sports, Science and Technology, Japan. ",

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AU - Hirose, Susumu

AU - Yasuhara, Akira

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N2 - A surface in a smooth 4-manifold is called flexible if, for any diffeomorphism φ{symbol} on the surface, there is a diffeomorphism on the 4-manifold whose restriction on the surface is φ{symbol} and which is isotopic to the identity. We investigate a sufficient condition for a smooth 4-manifold M to include flexible knotted surfaces, and introduce a local operation in simply connected 4-manifolds for obtaining a flexible knotted surface from any knotted surface.

AB - A surface in a smooth 4-manifold is called flexible if, for any diffeomorphism φ{symbol} on the surface, there is a diffeomorphism on the 4-manifold whose restriction on the surface is φ{symbol} and which is isotopic to the identity. We investigate a sufficient condition for a smooth 4-manifold M to include flexible knotted surfaces, and introduce a local operation in simply connected 4-manifolds for obtaining a flexible knotted surface from any knotted surface.

KW - 4-dimensional manifold

KW - Knotted surface

KW - Mapping class group

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SP - 41

EP - 50

JO - Topology

JF - Topology

IS - 1

ER -

Surfaces in 4-manifolds and their mapping class groups

Abstract

Keywords

ASJC Scopus subject areas

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