PreprintarXiv licencearXiv
On the cobordism groups of O⟨ n⟩-manifolds
Abstract
Given a smooth manifold, a tangential O⟨ n ⟩-structure is a lift of the classifying map of its tangent bundle to BO⟨ n ⟩. An O⟨ n ⟩-manifold is a manifold equipped with an equivalence class of tangential O⟨ n ⟩-structures. The cases n=2 and n=4 recover the familiar notions of oriented and spin manifolds. Larger values of n furnish higher analogs of these with additional geometric properties. In this thesis, we calculate the 2-primary component of the cobordism groups of compact $O\langle n\rangle $-manifolds in a range of degrees, for n between 9 and 17. We derive various consequences for the boundaries of almost-closed manifolds.
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BibTeX
@misc{abdallah2026cobordism,
title = {{On the cobordism groups of $O\langle n\rangle$-manifolds}},
author = {Hassan H. Abdallah},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28804},
eprint = {2609.28804},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28804},
}
RIS
TY - UNPB
TI - On the cobordism groups of O⟨ n⟩-manifolds
AU - Hassan H. Abdallah
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28804
UR - https://arxiv.org/abs/2609.28804
AB - Given a smooth manifold, a tangential O⟨ n ⟩-structure is a lift of the classifying map of its tangent bundle to BO⟨ n ⟩. An O⟨ n ⟩-manifold is a manifold equipped with an equivalence class of tangential O⟨ n ⟩-structures. The cases n=2 and n=4 recover the familiar notions of oriented and spin manifolds. Larger values of n furnish higher analogs of these with additional geometric properties. In this thesis, we calculate the 2-primary component of the cobordism groups of compact $O\langle n\rangle $-manifolds in a range of degrees, for n between 9 and 17. We derive various consequences for the boundaries of almost-closed manifolds.
ER -