Volume 12, issue 4 (2012)

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T2-cobordism of quasitoric 4–manifolds

Soumen Sarkar

Algebraic & Geometric Topology 12 (2012) 2003–2025
Abstract

We show the ${\mathbb{T}}^{2}$–cobordism group of the category of 4–dimensional quasitoric manifolds is generated by the ${\mathbb{T}}^{2}$–cobordism classes of ${ℂℙ}^{2}$. We construct nice oriented ${\mathbb{T}}^{2}$ manifolds with boundary whose boundaries are the Hirzebruch surfaces. The main tool is the theory of quasitoric manifolds.

Keywords
torus action, quasitoric manifold, cobordism group
Primary: 55N22
Secondary: 57R90
Publication
Received: 11 May 2011
Revised: 2 April 2012
Accepted: 28 June 2012
Published: 28 October 2012
Authors
 Soumen Sarkar Department of Mathematical Sciences Korea Advanced Institute of Science and Technology 373-1 Guseong-dong, Yuseong-gu Daejeon-305701 Republic of Korea
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