The DOI matches its Crossref record; 29 of the 29 references it cites were found in a registry or an index.
The stable moduli space of Riemann surfaces: Mumford’s conjecture
Open accessAbstract
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] that the plus construction makes BΓ ∞ into an infinite loop space led to a stable homotopy version of Mumford's conjecture, stronger than the original [24].We prove the stronger version, relying on Harer's stability theorem [17], Vassiliev's theorem concerning spaces of functions with moderate singularities [46], [45] and methods from homotopy theory.
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Categories for the Working Mathematician
Lane, S. M. (1971) · Graduate Texts in Mathematics · doi:10.1007/978-1-4612-9839-7 · Cited by 8,817
Hirsch, M. W. (1976) · Graduate Texts in Mathematics · doi:10.1007/978-1-4684-9449-5 · Cited by 2,520
Quillen, D. (1973) · Lecture Notes in Mathematics · doi:10.1007/bfb0067053 · Cited by 1,971 · cited 1×
“We have the associated bisimplicial set N•F(∆e) and recall [33] that the realization of its diagonal is homeomorphic to either of its double realizations, | k 7→ NkF(∆e) | ∼= ∣∣ ` 7→ | k 7→ NkF(∆e) |∣∣ = ∣∣ ` 7→ B(F(∆e)) ∣∣ ∼= ∣∣ k 7→ | ` 7→ NkF(∆e) |∣∣ = ∣∣ k 7→ |NkF|∣∣ .”
Stable Mappings and Their Singularities
Golubitsky, M., & Guillemin, V. (1973) · Graduate Texts in Mathematics · doi:10.1007/978-1-4615-7904-5 · Cited by 1,963
Homotopy Limits, Completions and Localizations
Bousfield, A. K., & Kan, D. M. (1972) · Lecture Notes in Mathematics · doi:10.1007/978-3-540-38117-4 · Cited by 1,726
Calculus of Fractions and Homotopy Theory
Gabriel, P., & Zisman, M. (1967) · Springer eBooks · doi:10.1007/978-3-642-85844-4 · Cited by 1,275
Categories and cohomology theories
Segal, G. (1974) · Topology · doi:10.1016/0040-9383(74)90022-6 · Cited by 970
Partial Differential Relations
Gromov, M. (1986) · Springer eBooks · doi:10.1007/978-3-662-02267-2 · Cited by 964
Classifying spaces and spectral sequences
Segal, G. (1968) · Publications Mathématiques de l'IHÉS · doi:10.1007/bf02684591 · Cited by 764
Towards an Enumerative Geometry of the Moduli Space of Curves
Mumford, D. (1983) · Arithmetic and Geometry · doi:10.1007/978-1-4757-9286-7_12 · Cited by 650
Metadata
- Authors
- Madsen, I., & Weiss, M.
- Venue
- Annals of Mathematics
- Publisher
- Annals of Mathematics
- Published
- 2007-05-01
- Volume
- 165
- Issue
- 3
- Pages
- 843-941
- ISSN
- 0003-486X (ISSN-L)
- OpenAlex
- W2164439626
- Cited by
- 266
- References
- 29
- FWCI
- 27.69
- Type
- journal article
- Language
- en
- Open access
- bronze
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