𝕋2–cobordism of quasitoric 4–manifolds

Sarkar, Soumen

doi:10.2140/agt.2012.12.2003

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T²-cobordism of quasitoric 4–manifolds

Soumen Sarkar

Algebraic & Geometric Topology 12 (2012) 2003–2025

DOI: 10.2140/agt.2012.12.2003

Abstract

We show the $T^{2}$ –cobordism group of the category of 4–dimensional quasitoric manifolds is generated by the $T^{2}$ –cobordism classes of ${ℂ ℙ}^{2}$ . We construct nice oriented $T^{2}$ 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

Mathematical Subject Classification 2010

Primary: 55N22

Secondary: 57R90

References

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

Volume 12, issue 4 (2012)