Manifold structures on highly connected Poincaré complexes
Abstract
This paper constructs numerous examples of highly connected Poincaré complexes, each homotopy equivalent to a topological manifold yet not homotopy equivalent to any smooth manifold. Furthermore, we determine the homotopy type of any closed 2 k 2k -connected framed ( 4 k + 2 ) (4k+2) -manifold with Kervaire invariant one for k = 7 , 15 , 31 k=7,15,31 .
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Geometric and Algebraic Topology
Advanced Differential Geometry Research
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 5
- Pages
- 2245–2255
- Publication date
- 10 February 2026
- Language
- EN