Stable moduli spaces of high-dimensional manifolds
成果类型：
Article
署名作者：
Galatius, Soren; Randal-Williams, Oscar
署名单位：
Stanford University; University of Cambridge
刊物名称：
ACTA MATHEMATICA
ISSN/ISSBN：
0001-5962
DOI：
10.1007/s11511-014-0112-7
发表日期：
2014
页码：
257-377
关键词：
摘要：
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 S (n) xS (n) , in the limit . 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 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 after stabilisation using certain self-bordisms of P. The stable homology is identified with that of an infinite loop space.
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