J. D. Quigley

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math.AT2026

Infinite families of very exotic spheres with free $S^{1}$ - and $S^{3}$ -actions

Tilman Bauer, J. D. Quigley

There are two kinds of exotic spheres: bp spheres, which bound parallelizable manifolds, and non-bp spheres, or very exotic spheres, which do not. In the 1960s, W.-C. Hsiang showed…

math.AT2026

New simple $I^\cdot$ -torsion families of elements in the stable stems

Irina Bobkova, J. D. Quigley

We produce five 192-periodic infinite families of simple $I^\cdot$ -torsion elements in the stable homotopy groups of spheres with trivial image under the tmf-Hurewicz homomorphism. We a…

math.AT2025

Symmetries of exotic spheres via complex and quaternionic Mahowald invariants

Boris Botvinnik, J. D. Quigley

We use new homotopy-theoretic tools to prove the existence of smooth $U (1)$ - and $S p (1)$ -actions on infinite families of exotic spheres. Such families of spheres are propagated by…

Infinite families of very exotic spheres with free S1- and S3-actions

New simple I^⋅-torsion families of elements in the stable stems

Symmetries of exotic spheres via complex and quaternionic Mahowald invariants

Infinite families of very exotic spheres with free $S^{1}$ - and $S^{3}$ -actions

New simple $I^\cdot$ -torsion families of elements in the stable stems