The weak b-principle: Mumford conjecture
Algebraic Topology
2021-01-11 v1
Abstract
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.
Cite
@article{arxiv.2101.02748,
title = {The weak b-principle: Mumford conjecture},
author = {Rustam Sadykov},
journal= {arXiv preprint arXiv:2101.02748},
year = {2021}
}