3 papers
math.AT2026
Mayer Path Homology
Dilan Karaguler, Guo-Wei Wei
We introduce Mayer path homology, a new homology theory for directed path complexes obtained by equipping path complexes with an -nilpotent differential. The main novelty of thi…
math.AT2026
PETLS: PErsistent Topological Laplacian Software
Benjamin Jones, Guo-Wei Wei
Persistent topological Laplacians are operators that provide persistent Betti numbers and additional multiscale geometric information through the eigenvalues of the persistent topo…
math.GT2024
A Khovanov Laplacian and Khovanov Dirac for Knots and Links
Benjamin Jones, Guo-Wei Wei
Khovanov homology has been the subject of much study in knot theory and low dimensional topology since 2000. This work introduces a Khovanov Laplacian and a Khovanov Dirac to study…