J. D. Quigley

activity

20182026

collaborators

Showing math.ATShow all

5 papers · 1 filter

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.AT2024

New simple $η$ -torsion families of elements in the stable stems

Irina Bobkova, J. D. Quigley

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

math.AT2023

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…

math.AT2019

Real motivic and $C_{2}$ -equivariant Mahowald invariants

J. D. Quigley

We generalize the Mahowald invariant to the $R$ -motivic and $C_{2}$ -equivariant settings. For all $i > 0$ with $i \equiv 2, 3 mod 4$ , we show that the $R$ -motivic Mah…

math.AT2018

The motivic Mahowald invariant

J. D. Quigley

The classical Mahowald invariant is a method for producing nonzero classes in the stable homotopy groups of spheres from classes in lower stems. We study the Mahowald invariant in…

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

New simple η-torsion families of elements in the stable stems

Symmetries of exotic spheres via complex and quaternionic Mahowald invariants

Real motivic and C2​-equivariant Mahowald invariants

The motivic Mahowald invariant

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

New simple $η$ -torsion families of elements in the stable stems

Real motivic and $C_{2}$ -equivariant Mahowald invariants