Algebraic & Geometric Topology

Cobordisms of maps with singularities of given class

Yoshifumi Ando

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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 np) 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 np2.

Article information

Source
Algebr. Geom. Topol., Volume 8, Number 4 (2008), 1989-2029.

Dates
Received: 6 June 2006
Revised: 18 August 2008
Accepted: 10 September 2008
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796922

Digital Object Identifier
doi:10.2140/agt.2008.8.1989

Mathematical Reviews number (MathSciNet)
MR2449006

Zentralblatt MATH identifier
1172.57013

Subjects
Primary: 57R45: Singularities of differentiable mappings
Secondary: 57R90: Other types of cobordism [See also 55N22] 58A20: Jets

Keywords
singularity map cobordism stable homotopy

Citation

Ando, Yoshifumi. Cobordisms of maps with singularities of given class. Algebr. Geom. Topol. 8 (2008), no. 4, 1989--2029. doi:10.2140/agt.2008.8.1989. https://projecteuclid.org/euclid.agt/1513796922


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