The stable mapping class group and Q(ℂP∞+)

By I. Madsen, Ulrike Tillmann. 2001

98 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/3a2ff50fafa2a4681952ae7cd40c407e45850bd1

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In Applied Mathematics

In Geometry and Topology

In Management Science and Operations Research

Citations in the corpus

A vanishing theorem for characteristic classes of odd-dimensional manifold bundles (2009, methodology): “Under the adjunction between the functors Σ and Ω, αE corresponds to a map B → Ω MTSO(n), which is the original Madsen-Tillmann map studied in [24], [25], [17].”
The homotopy type of the cobordism category (2006, background): “The Thom spaces (one-point compactifications) Th(U ? d,n ) form the spectrum MT (d) as n varies.”
The stable moduli space of Riemann surfaces: Mumford's conjecture (2002, background): “logical line bundle Ln. There is a map α∞ from Z × BΓ+ ∞ to ∞CP∞−1 constructed and examined in considerable detail in [ 22 ].”
Homological stability for the mapping class groups of non-orientable surfaces (2006, background): “We rely however on [19] for the connectivity of the complex of all circles in a surface to prove the last part of Theorem A. Theorem A also holds verbatim for mapping class groups of non-orientable surfaces with a fixed number s of punctures, which can be permutable or not.”
The structure of 2D semi-simple field theories (2007, background): “Madsen and Weiss prove an integral version, identifying the homotopy type of the group completion of the topological monoid Mg with the infinite loop space ∞CP∞−1 of the Madsen–Tillmann spectrum [25].”
Cohomological structure of the mapping class group and beyond (2005, result): “We also would like to mention fundamental results of Tillmann [104] and Madsen and Tillmann [ 63 ].”