relative_homology
#
This module contains a lazy implementation of a relative homology, $H_1(S,Sigma; R)$, where $S$ is a similarity surface, $Sigma$ is the singularities or vertices, and $R$ is a ring.
This implementation works for finite or infinite surfaces. For infinite surfaces, we define relative homology formally. It is simply $R^E$ where $E$ is the edge set modulo equivalences of two types: 1) If $e$ is an edge, and $e’$ is its opposite edge oriented counterclockwise from the polygon they bound then $e+e’=0$ in homology. 2) The sum of edges around a polygon is zero.
- class flatsurf.geometry.relative_homology.RelativeHomology(surface, base_ring=Integer Ring)[source]#
- Element#
alias of
RelativeHomologyClass