Stability of the homology of the moduli spaces of Riemann surfaces with spin structure

DOI10.1007/BF01446896zbMath0715.57004MaRDI QIDQ752546

John L. Harer

Publication date: 1990

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164688

zbMATH Keywords

Picard groupArf invariantfermionic string theoryconfiguration of simple closed curves on a surfacehomology of the spin moduli spaces of Riemann surfaces with spin structurespin mapping class groups

Mathematics Subject Classification ID

General low-dimensional topology (57M99) Families, moduli of curves (algebraic) (14H10) Teichmüller theory for Riemann surfaces (30F60) Riemann surfaces; Weierstrass points; gap sequences (14H55) Homology of classifying spaces and characteristic classes in algebraic topology (55R40) Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35) Differential topological aspects of diffeomorphisms (57R50)

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Local maxima of the systole function, Mod~2 homology of the stable spin mapping class group, Decoupling Decorations on Moduli Spaces of Manifolds, \(C^1\) actions on the circle of finite index subgroups of \(\mathrm{Mod}(\Sigma_g)\), \(\mathrm{Aut}(F_n)\), and \(\mathrm{Out}(F_n)\), The unstable integral homology of the mapping class groups of a surface with boundary, The homotopy type of the cobordism category, A heuristic for the distribution of point counts for random curves over a finite field, The Picard group of the moduli space of \(r\)-spin Riemann surfaces, The second rational homology group of the moduli space of curves with level structures, Universal moduli spaces of Riemann surfaces, The geometry of maximal components of the \(\mathsf{PSp}(4, \mathbb{R})\) character variety, Monoids of moduli spaces of manifolds, Moduli of curves and spin structures via algebraic geometry, ON THE GEOMETRY OF $\overline{S}_2$, Surfaces in the complex projective plane and their mapping class groups, On diffeomorphisms over surfaces trivially embedded in the \(4\)-sphere

Cites Work

• The second homology group of the mapping class group of an orientable surface
• Stability of the homology of the mapping class groups of orientable surfaces
• Homology stability for \(GL_n\) of a Dedekind domain
• Spherical posets and homology stability for \(O_ n,\)//n
• Stability for homology of the general linear group of a local ring
• On the Kervaire obstruction
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