Geodesic
Homological stability for diffeomorphism groups of high-dimensional handlebodies
Perlmutter, Nathan1
1 Department of Mathematics, Stanford University, Stanford, CA, United States
Algebraic and Geometric Topology, Tome 18 (2018) no. 5, pp. 2769-2820

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We prove a homological stability theorem for the diffeomorphism groups of high-dimensional manifolds with boundary, with respect to forming the boundary connected sum with the product Dp+1 × Sq for |q − p| < min{p − 2,q − 3}. In a recent joint paper with B Botvinnik, we prove that there is an isomorphism

in the case that n ≥ 4. By combining this “stable homology” calculation with the homological stability theorem of this paper, we obtain the isomorphism

in the case that k ≤ 1 2(g − 4).

DOI : 10.2140/agt.2018.18.2769
Classification : 57R15, 57R50, 57R65, 57S05
Keywords: manifolds, homological stability, moduli spaces

Perlmutter, Nathan 1

1 Department of Mathematics, Stanford University, Stanford, CA, United States 
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Perlmutter, Nathan. Homological stability for diffeomorphism groups of high-dimensional handlebodies. Algebraic and Geometric Topology, Tome 18 (2018) no. 5, pp. 2769-2820. doi: 10.2140/agt.2018.18.2769

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