KSp-characteristic classes determine Spinh cobordism
Abstract
A classic result of Anderson, Brown, and Peterson states that the cobordism spectrum MSpin (respectively, MSpin$^c$) splits as a sum of Eilenberg--Mac Lane spectra and connective covers of real K-theory (respectively, complex K-theory) at 2. We develop a theory of symplectic K-theory classes and use these to build an explicit splitting for MSpin$^h$ in terms of Eilenberg--Mac Lane spectra and spectra related to symplectic K-theory. This allows us to determine the Spin$^h$ cobordism groups systematically. We also prove that two Spin$^h$-manifolds are cobordant if and only if their underlying unoriented manifolds are cobordant and their KSp-characteristic numbers agree.
Fields of Study & Subjects
Geometric and Algebraic Topology
Homotopy and Cohomology in Algebraic Topology
Ophthalmology and Eye Disorders
Publication details
- Journal / source
- Algebraic & Geometric Topology
- Volume
- 26
- Issue
- 2
- Pages
- 485–551
- Publication date
- 11 February 2026
- Language
- EN