On Fico's Lemmata and the homotopy type of certain gyrations

Sebastian Chenery

doi:10.1112/blms.70265

On Fico's Lemmata and the homotopy type of certain gyrations

Sebastian Chenery^*

^*Corresponding author for this work

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

Abstract

We undertake to determine the homotopy type of gyrations of sphere products and of connected sums, thereby generalising results known in earlier literature as ‘Fico's Lemmata’ which underpin gyrations in their original formulation from geometric topology. We provide applications arising from recasting these results into the modern homotopy theoretic setting.

Original language	English
Article number	e70265
Number of pages	22
Journal	Bulletin of the London Mathematical Society
Volume	58
Issue number	1
DOIs	https://doi.org/10.1112/blms.70265
Publication status	Published - 19 Jan 2026

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© 2026 The Author(s).

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AB - We undertake to determine the homotopy type of gyrations of sphere products and of connected sums, thereby generalising results known in earlier literature as ‘Fico's Lemmata’ which underpin gyrations in their original formulation from geometric topology. We provide applications arising from recasting these results into the modern homotopy theoretic setting.

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M3 - Article (Academic Journal)

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On Fico's Lemmata and the homotopy type of certain gyrations

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