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Media type:
E-Article
Title:
Homological stability for moduli spaces of high dimensional manifolds. I
Contributor:
Galatius, Søren;
Randal-Williams, Oscar
Published:
American Mathematical Society (AMS), 2017
Published in:
Journal of the American Mathematical Society, 31 (2017) 1, Seite 215-264
Language:
English
DOI:
10.1090/jams/884
ISSN:
0894-0347;
1088-6834
Origination:
Footnote:
Description:
We prove a homological stability theorem for moduli spaces of simply connected manifolds of dimension 2 n > 4 2n > 4 , with respect to forming connected sum with S n × S n S^n \times S^n . This is analogous to Harer’s stability theorem for the homology of mapping class groups. Combined with previous work of the authors, it gives a calculation of the homology of the moduli spaces of manifolds diffeomorphic to connected sums of S n × S n S^n \times S^n in a range of degrees.