Embedding 3-manifolds with circle actions

Hillman, J.

doi:10.1090/S0002-9939-09-09985-7

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: Constraints on the Seifert invariants of orientable 3-manifolds which admit fixed-point free -actions and embed in $\mathbb{R}^4$ are given. In particular, the generalized Euler invariant of the orbit fibration is determined up to sign by the base orbifold unless $H_1(M;\mathbb{Z})$ is torsion free, in which case it can take at most one nonzero value (up to sign). An $\mathbb{H}^2\times\mathbb{E}^1$ -manifold with base orbifold $B=S^2(\alpha_1,\dots,\alpha_r)$ where all cone point orders are odd embeds in $\mathbb{R}^4$ if and only if its Seifert data is skew-symmetric.

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