Circle actions on simply connected 5-manifolds

János Kollár

doi:10.1016/j.top.2006.01.003

Circle actions on simply connected 5-manifolds

János Kollár

Mathematics

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

26 Scopus citations

Abstract

The aim of this paper is to study compact 5-manifolds which admit fixed point free circle actions. The first result implies that the torsion in the second homology and the second Stiefel-Whitney class have to satisfy strong restrictions. We then show that for simply connected 5-manifolds these restrictions are necessary and sufficient.

Original language	English (US)
Pages (from-to)	643-671
Number of pages	29
Journal	Topology
Volume	45
Issue number	3
DOIs	https://doi.org/10.1016/j.top.2006.01.003
State	Published - May 2006

All Science Journal Classification (ASJC) codes

Geometry and Topology

Keywords

5-manifold
Circle action
Sasakian geometry
Seifert bundle

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10.1016/j.top.2006.01.003

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title = "Circle actions on simply connected 5-manifolds",

abstract = "The aim of this paper is to study compact 5-manifolds which admit fixed point free circle actions. The first result implies that the torsion in the second homology and the second Stiefel-Whitney class have to satisfy strong restrictions. We then show that for simply connected 5-manifolds these restrictions are necessary and sufficient.",

keywords = "5-manifold, Circle action, Sasakian geometry, Seifert bundle",

author = "J{\'a}nos Koll{\'a}r",

note = "Funding Information: I thank A. Adem, Ch. Boyer, K. Galicki, Z. Szab{\'o} and W. Tuschmann for useful conversations and e-mails. Research was partially supported by the NSF under Grant numbers DMS-0200883 and DMS-0500198.",

year = "2006",

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language = "English (US)",

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T1 - Circle actions on simply connected 5-manifolds

AU - Kollár, János

N1 - Funding Information: I thank A. Adem, Ch. Boyer, K. Galicki, Z. Szabó and W. Tuschmann for useful conversations and e-mails. Research was partially supported by the NSF under Grant numbers DMS-0200883 and DMS-0500198.

PY - 2006/5

Y1 - 2006/5

N2 - The aim of this paper is to study compact 5-manifolds which admit fixed point free circle actions. The first result implies that the torsion in the second homology and the second Stiefel-Whitney class have to satisfy strong restrictions. We then show that for simply connected 5-manifolds these restrictions are necessary and sufficient.

AB - The aim of this paper is to study compact 5-manifolds which admit fixed point free circle actions. The first result implies that the torsion in the second homology and the second Stiefel-Whitney class have to satisfy strong restrictions. We then show that for simply connected 5-manifolds these restrictions are necessary and sufficient.

KW - 5-manifold

KW - Circle action

KW - Sasakian geometry

KW - Seifert bundle

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VL - 45

SP - 643

EP - 671

JO - Topology

JF - Topology

IS - 3

ER -

Circle actions on simply connected 5-manifolds

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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