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The Weak b-principle: Mumford Conjecture

Published online by Cambridge University Press:  20 November 2018

Rustam Sadykov
Rustam Sadykov*
Affiliation:
Department of Mathematics, CINVESTAV, Av. Instituto Politecnico Nacional 2508, Col. San Pedro Zacatenco, Mexico, D.F. CP 07360 e-mail: rstsdk@gmail.com
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Abstract

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In this note we introduce and study a new class of maps called oriented colored broken submersions. This is the simplest class of maps that satisfies a version of the $b$–principle and in dimension 2 approximates the class of oriented submersions well in the sense that every oriented colored broken submersion of dimension 2 to a closed simply connected manifold is bordant to a submersion. We show that the Madsen–Weiss theorem (the standard Mumford Conjecture) fits a general setting of the $b$–principle, namely, a version of the $b$–principle for oriented colored broken submersions together with the Harer stability theorem and Miller–Morita theorem implies the Madsen–Weiss theorem.

Keywords

55N2053C23generalized cohomology theoriesfold singularitiesh-principleinfinite loop spaces
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 68 , Issue 2 , 01 April 2016 , pp. 463 - 480
Copyright
Copyright © Canadian Mathematical Society 2016

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