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

Madsen, Ib; Tillmann, Ulrike

doi:10.1007/pl00005807

Cited by 66 publications

(68 citation statements)

References 4 publications

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“…Since α ∞ is an infinite loop map by [24], the theorem identifies the generalized cohomology theory determined by Z × BΓ + ∞ to be the one associated with the spectrum CP ∞ − 1 . To see that Theorem 1.1 verifies Mumford's conjecture we consider the homotopy fibration sequence of [37],…”

Section: Is a Homotopy Equivalencementioning

confidence: 99%

The stable moduli space of Riemann surfaces: Mumford’s conjecture

2007

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D. Mumford conjectured in [33] that the rational cohomology of the stable moduli space of Riemann surfaces is a polynomial algebra generated by certain classes κ i of dimension 2i. For the purpose of calculating rational cohomology, one may replace the stable moduli space of Riemann surfaces by BΓ ∞ , where Γ ∞ is the group of isotopy classes of automorphisms of a smooth oriented connected surface of "large" genus. Tillmann's theorem [44]

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Section: Is a Homotopy Equivalencementioning

confidence: 99%

The stable moduli space of Riemann surfaces: Mumford’s conjecture

2007

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“…These categories and their higher dimensional analogues have been studied extensively because of their fundamental relationship with conformal field theories and Mumford's conjecture [27,47].…”

Section: The Props Isomorphismmentioning

confidence: 99%

String topology of classifying spaces

Chataur

Menichi

2012

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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Abstract. Let G be a finite group or a compact connected Lie group and let BG be its classifying space. Let LBG := map(S 1 , BG) be the free loop space of BG i.e. the space of continuous maps from the circle S 1 to BG. The purpose of this paper is to study the singular homology H * (LBG) of this loop space. We prove that when taken with coefficients in a field the homology of LBG is a homological conformal field theory. As a byproduct of our main theorem, we get a Batalin-Vilkovisky algebra structure on the cohomology H * (LBG). We also prove an algebraic version of this result by showing that the Hochschild cohomology HH

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“…We are aware that there has been a correction to this paper in [11], but our indices are very simple and there is no difference.…”

Section: Proposition 42 the Composition Bomentioning

confidence: 99%

The homology of the stable nonorientable mapping class group

Randal-Williams¹

2008

Algebr. Geom. Topol.

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Combining results of Wahl, Galatius-Madsen-Tillmann-Weiss and Korkmaz one can identify the homotopy-type of the classifying space of the stable non-orientable mapping class group N∞ (after plus-construction). At odd primes p, the Fp-homology coincides with that of Q 0 (H P ∞ + ), but at the prime 2 the result is less clear. We identify the F 2 -homology as a Hopf algebra in terms of the homology of well-known spaces. As an application we tabulate the integral stable homology of N∞ in degrees up to six.As in the oriented case, not all of these cohomology classes have a geometric interpretation. We determine a polynomial subalgebra of H * (N∞; F 2 ) consisting of geometrically-defined characteristic classes.

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

Cited by 66 publications

References 4 publications

The stable moduli space of Riemann surfaces: Mumford’s conjecture

The stable moduli space of Riemann surfaces: Mumford’s conjecture

String topology of classifying spaces

The homology of the stable nonorientable mapping class group

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