Volume 8, issue 4 (2008)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Cobordisms of maps with singularities of given class

Yoshifumi Ando

Algebraic & Geometric Topology 8 (2008) 1989–2029
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 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 p 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