Singular fibers and 4-dimensional cobordism group

Osamu Saeki

Vol. 248 (2010), No. 1, 233–256

DOI: 10.2140/pjm.2010.248.233

Abstract

Using the technique of singular fibers of C^∞ stable maps, we give a new proof to the theorem, originally due to Rohlin, that the oriented cobordism group of 4-dimensional manifolds is infinite cyclic and is generated by the cobordism class of the complex projective plane. A byproduct is a new and transparent proof of the signature formula, originally due to T. Yamamoto and the author, for 4-dimensional manifolds in terms of singular fibers.

Keywords

singular fiber, stable map, cobordism group, signature, complex projective plane

Mathematical Subject Classification 2000

Primary: 57R45

Secondary: 57R75

Milestones

Received: 2 August 2009

Revised: 19 October 2009

Accepted: 30 November 2009

Published: 1 October 2010