Homological stability for moduli spaces of high dimensional manifolds. I

Galatius, Søren¹ ; Randal-Williams, Oscar²

¹ Department of Mathematics, Stanford University, Stanford, California 94305
² Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, United Kingdom

Journal of the American Mathematical Society, Tome 31 (2018) no. 1, pp. 215-264

Résumé

We prove a homological stability theorem for moduli spaces of simply connected manifolds of dimension $2n > 4$, with respect to forming connected sum with $S^n \times S^n$. 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 $S^n \times S^n$ in a range of degrees.

Détail

DOI : 10.1090/jams/884

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