Stable moduli spaces of high-dimensional manifolds
By Søren Galatius, O. Randal-Williams. 2012
103 citations recorded by the source corpus.
We prove an analogue of the Madsen–Weiss theorem for high-dimensional manifolds. In particular, we explicitly describe the ring of characteristic classes of smooth fibre bundles whose fibres are connected sums of g copies of Sn×Sn, in the limit $${g \to \infty}$$g→∞. Rationally it is a polynomial ring in certain explicit generators, giving a high-dimensional analogue of Mumford’s conjecture.More generally, we study a moduli space $${\mathcal{N}(P)}$$N(P) of those null-bordisms of a fixed (2n–1)-dimensional manifold P which are (n–1)-connected relative to P. We determine the homology of $${\mathcal{N}(P)}$$N(P) after stabilisation using certain self-bordisms of P. The stable homology is identified with that of an infinite loop space.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c855759a03d730125f77af1e6b609f2012e001a1
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In Geometry and Topology
In Mathematical Physics
- B. Botvinnik
- Johannes Ebert
- O. Randal-Williams
- Nathalie Wahl
- Søren Galatius
- Michael Weiss
- Pedro Boavida de Brito
Citations in the corpus
- Infinite loop spaces and positive scalar curvature (2014, methodology): “Thirdly, even if the results of [21] did apply to this stabilisation, we must show that there is a spin cobordism W : ∅ S2n−1 whose structure map l : W → BSpin(2n) is n-connected and which in addition satisfies the conditions given in Section 4.”