Simple homotopy types of smooth four-manifolds with finite fundamental group

Daniel Kasprowski; John Nicholson

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arXiv · 2610.32706

Simple homotopy types of smooth four-manifolds with finite fundamental group

Daniel Kasprowski·John Nicholson

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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 $S^2\times S^2$. Our explicit examples have remarkably large fundamental groups; in particular, the smallest examples we obtain have fundamental groups of order roughly $10^{10^{42}}$.

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Daniel Kasprowski, John Nicholson. 2026-10-23. Simple homotopy types of smooth four-manifolds with finite fundamental group. https://arxiv.org/abs/2610.32706

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