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2009 Bordism groups of solutions to differential relations
Rustam Sadykov
Algebr. Geom. Topol. 9(4): 2311-2347 (2009). DOI: 10.2140/agt.2009.9.2311

Abstract

In terms of category theory, the Gromov homotopy principle for a set valued functor F asserts that the functor F can be induced from a homotopy functor. Similarly, we say that the bordism principle for an abelian group valued functor F holds if the functor F can be induced from a (co)homology functor.

We examine the bordism principle in the case of functors given by (co)bordism groups of maps with prescribed singularities. Our main result implies that if a family J of prescribed singularity types satisfies certain mild conditions, then there exists an infinite loop space ΩBJ such that for each smooth manifold W the cobordism group of maps into W with only J–singularities is isomorphic to the group of homotopy classes of maps [W,ΩBJ]. The spaces ΩBJ are relatively simple, which makes explicit computations possible even in the case where the dimension of the source manifold is bigger than the dimension of the target manifold.

Citation

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Rustam Sadykov. "Bordism groups of solutions to differential relations." Algebr. Geom. Topol. 9 (4) 2311 - 2347, 2009. https://doi.org/10.2140/agt.2009.9.2311

Information

Received: 25 December 2006; Revised: 18 May 2009; Accepted: 19 May 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1179.57044
MathSciNet: MR2558312
Digital Object Identifier: 10.2140/agt.2009.9.2311

Subjects:
Primary: 53C23, 55N20
Secondary: 57R45

Rights: Copyright © 2009 Mathematical Sciences Publishers

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