PreprintCC BY 4.0arXiv
Simple homotopy types of smooth four-manifolds with finite fundamental group
Abstract
We construct closed smooth $4$-manifolds with finite fundamental group which are homotopy equivalent but not simple homotopy equivalent, even after taking a connected sum with copies of S2× S2. Our explicit examples have remarkably large fundamental groups; in particular, the smallest examples we obtain have fundamental groups of order roughly 101042.
Related
- Smooth manifolds homotopy equivalent to products of spheres
- On smooth and bundle structures on topological manifolds homotopy equivalent to S4k−1-bundles over S4k
- Growth of Simple Closed Geodesics in Finite-Volume Hyperbolic Manifolds
- Homotopy rigidity for quasitoric manifolds over a product of simplices
- Rational homotopy theory of flag manifolds
BibTeX
@misc{kasprowski2026simple,
title = {{Simple homotopy types of smooth four-manifolds with finite fundamental group}},
author = {Daniel Kasprowski and John Nicholson},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32706},
eprint = {2610.32706},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32706},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Simple homotopy types of smooth four-manifolds with finite fundamental group
AU - Daniel Kasprowski
AU - John Nicholson
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32706
UR - https://arxiv.org/abs/2610.32706
AB - We construct closed smooth $4$-manifolds with finite fundamental group which are homotopy equivalent but not simple homotopy equivalent, even after taking a connected sum with copies of S^2× S^2. Our explicit examples have remarkably large fundamental groups; in particular, the smallest examples we obtain have fundamental groups of order roughly 10^10^42.
ER -