L. Williams

collaborators

4 papers

math.AT2026

Equivariant Framed 1-Manifolds and the Pontryagin-Thom Isomorphism

Lucas Williams

The Pontryagin-Thom theorem gives an isomorphism between the cobordism group of framed $n$ -dimensional manifolds, $I ¨ _{n}$ , and the $n^{t h}$ stable homotopy group of the sphere spect…

math.AT2025

Comparing Periodic Point Invariants for Parameterized Families of Maps

Lucas Williams

We compare different periodic point invariants for families of maps parameterized over a compact manifold. Malkiewich and Ponto showed that, in the case of a single map, the Fuller…

math.AT2025

Scissors congruence K-theory for equivariant manifolds

Mona Merling, Ming Ng, Julia Semikina +2

We introduce a scissors congruence $K$ -theory spectrum which lifts the equivariant scissors congruence groups for compact $G$ -manifolds with boundary, and we show that on $I ¨ _{0}$ th…

math.AT2025

The Pontryagin-Thom theorem for families of framed equivariant manifolds

Lucas Williams

The Pontryagin-Thom theorem gives an isomorphism from the cobordism group of framed $n$ -manifolds to the $n$ th stable homotopy group of the sphere spectrum. In this paper, we prove…