On Fico's Lemmata and the Homotopy Type of Certain Gyrations

TL;DR

This paper investigates the homotopy types of gyrations in sphere products and connected sums, extending Fico's Lemmata within a modern homotopy theory framework to deepen understanding in geometric topology.

Contribution

It generalizes Fico's Lemmata to a homotopy theoretic setting, providing new insights into the topology of gyrations in complex manifolds.

Findings

Homotopy types of gyrations are characterized for sphere products.

Results extend classical lemmas to modern homotopy theory.

Applications include new perspectives in geometric topology.

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.