Embedding -manifolds with circle actions

Author:
J. A. Hillman

Journal:
Proc. Amer. Math. Soc. **137** (2009), 4287-4294

MSC (2000):
Primary 57N10; Secondary 57N13

DOI:
https://doi.org/10.1090/S0002-9939-09-09985-7

Published electronically:
July 16, 2009

MathSciNet review:
2538589

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Abstract | References | Similar Articles | Additional Information

Abstract: Constraints on the Seifert invariants of orientable 3-manifolds which admit fixed-point free -actions and embed in are given. In particular, the generalized Euler invariant of the orbit fibration is determined up to sign by the base orbifold unless is torsion free, in which case it can take at most one nonzero value (up to sign). An -manifold with base orbifold where all cone point orders are odd embeds in if and only if its Seifert data is skew-symmetric.

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Additional Information

**J. A. Hillman**

Affiliation:
School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia

Email:
jonh@maths.usyd.edu.au

DOI:
https://doi.org/10.1090/S0002-9939-09-09985-7

Keywords:
Embedding,
Euler invariant,
linking pairing,
Seifert bundle

Received by editor(s):
January 19, 2009

Received by editor(s) in revised form:
April 2, 2009

Published electronically:
July 16, 2009

Additional Notes:
This paper began as a 1998 University of Sydney Research Report, but the main result was obtained while the author was visiting the University of Durham as the Grey College Mathematics Fellow for Michaelmas Term of 2008.

Communicated by:
Daniel Ruberman

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.