arXiv subjects

Jesse Moeller

Publications and source records attributed to Jesse Moeller.

2 recordsLinked to original sources

arXiv2020

Diagrams of *-Trisections

In this note, we provide a generalization for the definition of a trisection of a 4-manifold with boundary. We demonstrate the utility of this more general definition by finding a trisection diagram for the Cacime Surface, and also by finding a trisection-theoretic way to perform logarithmic surgery. In addition, we describe how to perform 1-surgery on closed trisections. The insight gained from this description leads us to the classification of an infinite family of genus three trisections. We include an appendix where we extend two classic results for relative trisections for the case when the trisection surface is closed.

math.GT↗

arXiv2016

Magnetic Laplacians of locally exact forms on the Sierpinski Gasket

We give a mathematically rigorous construction of a magnetic Schrödinger operator corresponding to a field with flux through finitely many holes of the Sierpinski Gasket. The operator is shown to have discrete spectrum accumulating at $\infty$, and it is shown that the asymptotic distribution of eigenvalues is the same as that for the Laplacian. Most eigenfunctions may be computed using gauge transformations corresponding to the magnetic field and the remainder of the spectrum may be approximated to arbitrary precision by using a sequence of approximations by magnetic operators on finite graphs.

math.SP↗