The Weak b-principle: Mumford Conjecture

Sadykov, Rustam

Canadian journal of mathematics, Tome 68 (2016) no. 2, pp. 463-480

Résumé

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.

Détail

DOI : 10.4153/CJM-2015-003-4

Mots-clés : 55N20, 53C23, generalized cohomology theories, fold singularities, h-principle, infinite loop spaces

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