J. D. Quigley

collaborators

4 papers

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.KT2025

Very effective algebraic and hermitian K-theory of the cyclic group of order two

Prerna Dhankhar, Rebecca Field, Arjun Nigam +2

We compute the $2$ -completed integral motivic homology, effective algebraic K-theory, and very effective hermitian K-theory of the geometric classifying space of the cyclic group o…

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

Very effective algebraic and hermitian K-theory of the cyclic group of order two

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