Manifold structures on highly connected Poincar\'e complexes
Algebraic Topology
2025-08-21 v2 Geometric Topology
Abstract
This paper constructs numerous examples of highly connected Poincar\'{e} 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 -connected framed -manifold with Kervaire invariant one for .
Cite
@article{arxiv.2507.23228,
title = {Manifold structures on highly connected Poincar\'e complexes},
author = {Wen Shen},
journal= {arXiv preprint arXiv:2507.23228},
year = {2025}
}