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Mathematics > Algebraic Topology

arXiv:1007.5105 (math)
[Submitted on 29 Jul 2010 (v1), last revised 26 Apr 2016 (this version, v4)]

Title:Orientability and equivariant oriented cobordism of 2-torus manifolds

Authors:Soumen Sarkar
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Abstract:We give a necessary and sufficient condition for the orientability of a locally standard 2-torus manifold with a fixed point which generalizes previous results of Nakayama-Nishimura in 2005 and Soprunova-Sottile in 2013. We construct manifolds with boundary where the boundary is a disjoint union of locally standard 2-torus manifolds. We discuss equivariant oriented cobordism class of locally standard 2-torus manifolds.
Comments: 17 pages, 6 figures, Previous version contained two parts. 1. Oriented cobordism of $\CP^{2k+1}$ which is available in http://arxiv.org/abs/1011.0554. 2. oriented cobordism of $\RP^{2k+1}$. The results and constructions of second part are generalized to the category of 2-torus manifolds in the present version
Subjects: Algebraic Topology (math.AT)
MSC classes: 55N22, 57R90
Cite as: arXiv:1007.5105 [math.AT]
  (or arXiv:1007.5105v4 [math.AT] for this version)
  https://doi.org/10.48550/arXiv.1007.5105

Submission history

From: Soumen Sarkar [view email]
[v1] Thu, 29 Jul 2010 04:43:42 UTC (16 KB)
[v2] Thu, 2 Sep 2010 08:08:59 UTC (16 KB)
[v3] Fri, 3 Sep 2010 05:09:41 UTC (16 KB)
[v4] Tue, 26 Apr 2016 16:42:13 UTC (24 KB)
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