Repository logo
 

Abelian quotients of mapping class groups of highly connected manifolds


Change log

Authors

Galatius, S 
Randal-Williams, Oscar  ORCID logo  https://orcid.org/0000-0002-7479-2878

Abstract

We compute the abelianisations of the mapping class groups of the manifolds Wg2n=g(Sn×Sn) for n≥3 and g≥5. The answer is a direct sum of two parts. The first part arises from the action of the mapping class group on the middle homology, and takes values in the abelianisation of the automorphism group of the middle homology. The second part arises from bordism classes of mapping cylinders and takes values in the quotient of the stable homotopy groups of spheres by a certain subgroup which in many cases agrees with the image of the stable J-homomorphism. We relate its calculation to a purely homotopy theoretic problem.

Description

Keywords

math.AT, math.AT, 55N22, 57R15, 55P47, 55Q10, 57S05

Journal Title

Mathematische Annalen

Conference Name

Journal ISSN

0025-5831
1432-1807

Volume Title

Publisher

Springer Science and Business Media LLC