Cobordisms of maps with singularities of given class

Ando, Yoshifumi

doi:10.2140/agt.2008.8.1989

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Cobordisms of maps with singularities of given class

Yoshifumi Ando

Algebraic & Geometric Topology 8 (2008) 1989–2029

DOI: 10.2140/agt.2008.8.1989

Abstract

Let $P$ be a smooth manifold of dimension $p$ . We will describe the group of all cobordism classes of smooth maps of $n$ –dimensional closed manifolds into $P$ with singularities of given class (including all fold singularities if $n \geq p$ ) in terms of certain stable homotopy groups by applying the homotopy principle on the existence level, which is assumed to hold for those smooth maps. It will enable us to construct an explicit classifying space for this cobordism group in the dimensions $n < p$ and $n \geq p \geq 2$ .

Dedicated to Professor Takao Matumoto on his sixtieth birthday

Keywords

singularity, map, cobordism, stable homotopy

Mathematical Subject Classification 2000

Primary: 57R45

Secondary: 57R90, 58A20

References

Publication

Received: 6 June 2006

Revised: 18 August 2008

Accepted: 10 September 2008

Published: 28 October 2008

Authors

Yoshifumi Ando
Department of Mathematical Sciences Faculty of Science Yamaguchi University Yamaguchi 753-8512 Japan

Volume 8, issue 4 (2008)