The stable moduli space of Riemann surfaces: Mumford's conjecture
Ib Madsen, Michael S. Weiss
TL;DR
This paper proves Mumford's conjecture by fully determining the rational cohomology of the stable mapping class group, providing a comprehensive understanding of its integral cohomological structure.
Contribution
It offers a complete evaluation of the integral cohomological structure of the stable mapping class group, confirming Mumford's conjecture.
Findings
Verification of Mumford's conjecture on rational cohomology
Complete description of the integral cohomological structure
Advancement in understanding the topology of Riemann surfaces
Abstract
The main result of this paper amounts to a complete evaluation of the integral cohomological structure of the stable mapping class group. In particular it verifies the conjecture of D.Mumford about the rational cohomology of the stable mapping class group.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory · Geometric and Algebraic Topology