Resolutions of moduli spaces and homological stability
By O. Randal-Williams. 2009
82 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/d3c25f9e1db3eee11a73955174c061aa9e544c1d
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In Geometry and Topology
- O. Randal-Williams
- Nathalie Wahl
- Michael Weiss
- Pedro Boavida de Brito
- Søren Galatius
- Andrew Putman
- Steven V. Sam
- Johannes Ebert
In Mathematical Physics
- O. Randal-Williams
- Nathalie Wahl
- Michael Weiss
- Pedro Boavida de Brito
- Søren Galatius
- Andrew Putman
- Steven V. Sam
- Johannes Ebert
Citations in the corpus
- Spaces of smooth embeddings and configuration categories (2015, methodology): “This is inspired by some observations on configuration spaces due to Oscar Randal-Williams [30] which we learned by reading [37].”
- Hochschild homology of structured algebras (2011, unknown): “This is a consequence of Harer’s stability theorem ([23], with the improved range of [3,53] and [61] for punctures in S).”
- Homology of the moduli spaces and mapping class groups of framed, r‐Spin and Pin surfaces (2010, methodology): “Guide We prove the homological stability theorems for these tangential structures by applying the general stability theorems of [21].”
- Homological stability for automorphism groups (2014, background): “entable surface were dened to be embeddings with non-orientable or genus 0 complement. This restriction corresponds to the notion of a better 1-sided arc in [85, Sec. 3] as long as n2. (In [85] and [68], a choice was made not to allow genus 0 complement as it did not help|or hinder. As we will see, ”