The Weak b-principle: Mumford Conjecture
Canadian journal of mathematics, Tome 68 (2016) no. 2, pp. 463-480
Voir la notice de l'article provenant de la source Cambridge
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.
Mots-clés :
55N20, 53C23, generalized cohomology theories, fold singularities, h-principle, infinite loop spaces
Sadykov, Rustam. The Weak b-principle: Mumford Conjecture. Canadian journal of mathematics, Tome 68 (2016) no. 2, pp. 463-480. doi: 10.4153/CJM-2015-003-4
@article{10_4153_CJM_2015_003_4,
author = {Sadykov, Rustam},
title = {The {Weak} b-principle: {Mumford} {Conjecture}},
journal = {Canadian journal of mathematics},
pages = {463--480},
year = {2016},
volume = {68},
number = {2},
doi = {10.4153/CJM-2015-003-4},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2015-003-4/}
}
Cité par Sources :