Braidings of Self-Equivalences and Bordism

Ian Hambleton; Kursat Sozer

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arXiv · 2610.11110

Braidings of Self-Equivalences and Bordism

Ian Hambleton·Kursat Sozer

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Abstract

Let $M$ be a closed, smooth or topological $n$-manifold, with $n \geq 4$. We construct a homotopy highly cartesian square relating the space ${\mathcal E}(M (\ell))$ of homotopy self-equivalences of $M$ (in a suitable range) over the Postnikov $\ell$-sections of its stable normal microbundle, and an $(\infty + n)$-fold loop space representing an associated (normal) bordism theory. This implies the existence of braids of interlocking exact sequences involving the homotopy groups of ${\mathcal E}(M(\ell))$ and certain Lashof bordism groups, leading to a conceptual explanation and broad generalization of earlier work of Hambleton--Kreck for closed, oriented $4$-manifolds.

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Ian Hambleton, Kursat Sozer. 2026-10-08. Braidings of Self-Equivalences and Bordism. https://arxiv.org/abs/2610.11110

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