Year: 2026
Type: preprint
Abstract: We define a $d$-cube in a graph $G$ to be monophobic in $G$ if, whenever it supports a $d$-face of a discrete singular $d+1$-cube, it must also support another face. In many cases, the presence of such cubes implies the nontriviality of discrete cubical homology and homotopy groups associated with $G$. We describe several large classes of examples and characterize the property completely when $d=2$.
Source: arXiv (Cornell University)
Authors: Greene, Curtis, Jamil, Samira Sahar
Institution: Haverford College
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221807763