arXiv:0909.4278 Abstract | arXiv Analytics

arXiv:0909.4278 [math.AT]Abstract References Reviews Resources

Resolutions of moduli spaces and homological stability

Published 2009-09-23, updated 2014-10-21Version 4

We describe partial semi-simplicial resolutions of moduli spaces of surfaces with tangential structure. This allows us to prove a homological stability theorem for these moduli spaces, which often improves the known stability ranges and give explicit stability ranges in many new cases. In each of these cases the stable homology can be identified using the methods of Galatius, Madsen, Tillmann and Weiss.

Comments: 74 pages, 15 figures; V2: Warning, Completely Revised Version; V3: Removed discussion of configuration spaces; V4 Completely revised again, to appear in J. Eur. Math. Soc

Categories: math.AT, math.GT

Subjects: 55R40, 57R15, 57R50, 57M07, 20J06

Keywords: moduli spaces, partial semi-simplicial resolutions, explicit stability ranges, tangential structure, homological stability theorem

Related articles: Most relevant | Search more

arXiv:1408.1903 [math.AT] (Published 2014-08-08, updated 2014-08-29)

Homological Stability For The Moduli Spaces of Products of Spheres

Nathan Perlmutter

arXiv:2209.08148 [math.AT] (Published 2022-09-16)

Computations in the unstable homology of moduli spaces of Riemann surfaces

Carl-Friedrich Bödigheimer, Felix Boes, Florian Kranhold

arXiv:0905.2855 [math.AT] (Published 2009-05-18, updated 2009-07-27)

Monoids of moduli spaces of manifolds