PreprintCC0arXiv
Loop Space Splittings for Codimensional Sphere Bundles
Abstract
In this paper, we establish two loop decomposition theorems for sphere bundles of real vector bundles under appropriate connectivity and characteristic class assumptions. Specifically, we treat two families of sphere bundles: those arising from rank-(n−1) vector bundles and those from rank-(n−3) vector bundles over closed smooth n-manifolds.
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BibTeX
@misc{shen2026loop,
title = {{Loop Space Splittings for Codimensional Sphere Bundles}},
author = {Wen Shen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.03072},
eprint = {2606.03072},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.03072},
note = {CC0},
}
RIS
TY - UNPB
TI - Loop Space Splittings for Codimensional Sphere Bundles
AU - Wen Shen
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2606.03072
UR - https://arxiv.org/abs/2606.03072
AB - In this paper, we establish two loop decomposition theorems for sphere bundles of real vector bundles under appropriate connectivity and characteristic class assumptions. Specifically, we treat two families of sphere bundles: those arising from rank-(n−1) vector bundles and those from rank-(n−3) vector bundles over closed smooth n-manifolds.
ER -