3 papers
math.CO2026
PL standardness of the four-pentachoron census sphere Q
Vance Faber, Michael Murphy
We prove that the four-pentachoron homotopy \(4\)-sphere \(Q\) singled out in the census of Burke, Burton and Spreer is PL homeomorphic to the standard \(4\)-sphere. The key constr…
math.CO2025
The Trunk of the Restricted Flip Graph of Triangulated S^3
V. Faber, M. Murphy
Let (\mathcal{F}_M(n)) be the restricted flip graph of (n)-vertex triangulations of a closed connected (3)-manifold (M), whose edges are vertex-preserving (2)--(3) and (3)--(2) bis…
math.CO2019
Which Cubic Graphs have Quadrangulated Spherical Immersions?
Lowell Abrams, Yosef Berman, Vance Faber +1
We consider spherical quadrangulations -- spherical embeddings of multigraphs, possibly with loops, so that every face has boundary walk of length 4 -- in which all vertices have d…