#### 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