Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 18, Number 5 (2018), 2769-2820.
Homological stability for diffeomorphism groups of high-dimensional handlebodies
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 for . In a recent joint paper with B Botvinnik, we prove that there is an isomorphism
in the case that . By combining this “stable homology” calculation with the homological stability theorem of this paper, we obtain the isomorphism
in the case that .
Algebr. Geom. Topol., Volume 18, Number 5 (2018), 2769-2820.
Received: 23 April 2017
Revised: 11 March 2018
Accepted: 22 March 2018
First available in Project Euclid: 30 August 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57R15: Specialized structures on manifolds (spin manifolds, framed manifolds, etc.) 57R50: Diffeomorphisms 57R65: Surgery and handlebodies 57S05: Topological properties of groups of homeomorphisms or diffeomorphisms
Perlmutter, Nathan. Homological stability for diffeomorphism groups of high-dimensional handlebodies. Algebr. Geom. Topol. 18 (2018), no. 5, 2769--2820. doi:10.2140/agt.2018.18.2769. https://projecteuclid.org/euclid.agt/1535594422