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2018 Homological stability for diffeomorphism groups of high-dimensional handlebodies
Nathan Perlmutter
Algebr. Geom. Topol. 18(5): 2769-2820 (2018). DOI: 10.2140/agt.2018.18.2769

Abstract

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 D p + 1 × S q for | q p | < min { p 2 , q 3 } . In a recent joint paper with B Botvinnik, we prove that there is an isomorphism

colim g H ( BDiff ( ( D n + 1 × S n ) g , D 2 n ) ; ) H ( Q 0 B O ( 2 n + 1 ) n + ; )

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

H k ( BDiff ( ( D n + 1 × S n ) g , D 2 n ) ; ) H k ( Q 0 B O ( 2 n + 1 ) n + ; )

in the case that k 1 2 ( g 4 ) .

Citation

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Nathan Perlmutter. "Homological stability for diffeomorphism groups of high-dimensional handlebodies." Algebr. Geom. Topol. 18 (5) 2769 - 2820, 2018. https://doi.org/10.2140/agt.2018.18.2769

Information

Received: 23 April 2017; Revised: 11 March 2018; Accepted: 22 March 2018; Published: 2018
First available in Project Euclid: 30 August 2018

zbMATH: 06935820
MathSciNet: MR3848399
Digital Object Identifier: 10.2140/agt.2018.18.2769

Subjects:
Primary: 57R15, 57R50, 57R65, 57S05

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 5 • 2018
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