The Weak b-principle: Mumford Conjecture
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Published:2016-04-01
Issue:2
Volume:68
Page:463-480
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ISSN:0008-414X
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Container-title:Canadian Journal of Mathematics
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language:en
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Short-container-title:Can. j. math.
Abstract
AbstractIn 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.
Publisher
Canadian Mathematical Society
Subject
General Mathematics