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The Oriented Freudenthal Suspension Theorem
Abstract
The Freudenthal Suspension Theorem states that the connectivity of the unit map X→ΩΣX of the suspension-loop adjunction for a pointed space X is twice the connectivity of X itself. We extend this theorem to X being a pointed (∞,∞)-category, i.e. an oriented space in the sense of Gepner--Heine.
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BibTeX
@misc{geiß2026oriented,
title = {{The Oriented Freudenthal Suspension Theorem}},
author = {Thorger Geiß},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38949},
eprint = {2610.38949},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38949},
}
RIS
TY - UNPB
TI - The Oriented Freudenthal Suspension Theorem
AU - Thorger Geiß
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38949
UR - https://arxiv.org/abs/2610.38949
AB - The Freudenthal Suspension Theorem states that the connectivity of the unit map X→ΩΣX of the suspension-loop adjunction for a pointed space X is twice the connectivity of X itself. We extend this theorem to X being a pointed (∞,∞)-category, i.e. an oriented space in the sense of Gepner--Heine.
ER -