arXiv subjects

Nathaniel Stambaugh

Publications and source records attributed to Nathaniel Stambaugh.

3 recordsLinked to original sources

arXiv2016

Outer space for untwisted automorphisms of right-angled Artin groups

For a right-angled Artin group $A_Γ$, the untwisted outer automorphism group $U(A_Γ)$ is the subgroup of $Out(A_Γ)$ generated by all of the Laurence-Servatius generators except twists (where a {\em twist} is an automorphisms of the form $v\mapsto vw$ with $vw=wv$). We define a space $Σ_Γ$ on which $U(A_Γ)$ acts properly and prove that $Σ_Γ$ is contractible, providing a geometric model for $U(A_Γ)$ and its subgroups. We also propose a geometric model for all of $Out(A_Γ)$ defined by allowing more general markings and metrics on points of $Σ_Γ$.

math.GR↗

arXiv2013

Using symmetry to generate solutions to the Helmholtz equation inside an equilateral triangle

We prove that every solution of the Helmholtz equation within an equilateral triangle, which obeys the Dirichlet conditions on the boundary, is a member of one of four symmetry classes. We then show how solutions with different symmetries, or different energies, can be generated from any given solution using symmetry operators or a differential operator derived from symmetry considerations. Our method also provides a novel way of generating the ground state solution (that is, the solution with the lowest energy). Finally, we establish a correspondence between solutions in the equilateral and (30,60, 90) triangles.

physics.class-ph↗

arXiv2009

The automorphism group of a graph product with no SIL

We study the automorphisms of graph products of cyclic groups, a class of groups that includes all right-angled Coxeter and right-angled Artin groups. We show that the group of automorphism generated by partial conjugations is itself a graph product of cyclic groups providing its defining graph does not contain any separating intersection of links (SIL). In the case that all the cyclic groups are finite, this implies that the automorphism group is virtually CAT(0); it has a finite index subgroup which acts geometrically on a right-angled building.

math.GR↗