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Braidings of Self-Equivalences and Bordism
Abstract
Let M be a closed, smooth or topological n-manifold, with n ≥ 4. We construct a homotopy highly cartesian square relating the space ℰ(M (ℓ)) of homotopy self-equivalences of M (in a suitable range) over the Postnikov ℓ-sections of its stable normal microbundle, and an (∞ + 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 ℰ(M(ℓ)) 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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BibTeX
@misc{hambleton2026braidings,
title = {{Braidings of Self-Equivalences and Bordism}},
author = {Ian Hambleton and Kursat Sozer},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11110},
eprint = {2610.11110},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11110},
}
RIS
TY - UNPB
TI - Braidings of Self-Equivalences and Bordism
AU - Ian Hambleton
AU - Kursat Sozer
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11110
UR - https://arxiv.org/abs/2610.11110
AB - Let M be a closed, smooth or topological n-manifold, with n ≥ 4. We construct a homotopy highly cartesian square relating the space ℰ(M (ℓ)) of homotopy self-equivalences of M (in a suitable range) over the Postnikov ℓ-sections of its stable normal microbundle, and an (∞ + 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 ℰ(M(ℓ)) and certain Lashof bordism groups, leading to a conceptual explanation and broad generalization of earlier work of Hambleton--Kreck for closed, oriented $4$-manifolds.
ER -