Stable moduli spaces of high dimensional manifolds

Details Stable moduli spaces of high dimensional manifolds Stable moduli spaces of high dimensional manifolds

2012-01-17

arxiv.org/abs/1201.3527v1

Mathematics

Algebraic Topology

71 pages, 5 figures

Scientific paper

We prove an analogue of the Madsen-Weiss theorem for high dimensional manifolds. For example, we explicitly describe the ring of characteristic classes of smooth fibre bundles whose fibres are connected sums of g copies of S^n x S^n, in the limit as g tends to infinity. 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 N(P) of those null-bordisms of a fixed (2n-1)-dimensional manifold P which are highly connected relative to P. We determine the homology of N(P) after stabilisation using certain self-bordisms of P. The stable homology is identified with that of a certain infinite loop space.

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