Some Hermitian K-groups via geometric topology

Abstract

We compute the first two symplectic quadratic K-theory groups of the integers, or equivalently, the first two stable homology groups of the group of symplectic integral matrices preserving the standard quadratic refinement. The main novelty in our calculation lies in its method, which is based on high-dimensional manifold theory.

6 pages, to appear in Proceedings of the American Mathematical Society

References in corpus (1)

• Mapping class groups of highly connected $(4k+2)$-manifolds

Cited by in corpus (1)

• Mapping class groups of highly connected $(4k+2)$-manifolds