PreprintCC BY 4.0arXiv
A Cohomological Obstruction to the Existence of ϕ-Equivariant Maps
Abstract
Let ϕ: G→ H be a continuous homomorphism between compact Lie groups, let X be a G-space, and let Y be an H-space. We formulate a filtered change-of-groups obstruction to the existence of a ϕ-equivariant map X→ Y. We apply them to the inclusion of a finite cyclic group into the circle and to homomorphisms between tori acting coordinatewise on products of odd-dimensional spheres.
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BibTeX
@misc{paiva2026cohomological,
title = {{A Cohomological Obstruction to the Existence of $ϕ$-Equivariant Maps}},
author = {Thales Fernando Vilamaior Paiva},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.23230},
eprint = {2607.23230},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.23230},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Cohomological Obstruction to the Existence of ϕ-Equivariant Maps
AU - Thales Fernando Vilamaior Paiva
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2607.23230
UR - https://arxiv.org/abs/2607.23230
AB - Let ϕ: G→ H be a continuous homomorphism between compact Lie groups, let X be a G-space, and let Y be an H-space. We formulate a filtered change-of-groups obstruction to the existence of a ϕ-equivariant map X→ Y. We apply them to the inclusion of a finite cyclic group into the circle and to homomorphisms between tori acting coordinatewise on products of odd-dimensional spheres.
ER -