2025/12/15 by Anshu Agarwal, Agarwal, Anshu, Biplab Basak +2
Mathematics · #05C10 #52B70 #52C20 #57Q15 #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Secondary 05C15
paper · pdf · doi:10.48550/arxiv.2512.13135
openalex publication_date 2025/12/15 · openalex created_date 2025/12/17 · openalex updated_date 2026/07/28
A semi-equivelar gem of a PL d-manifold is a regular colored graph that represents the manifold and admits a regular embedding on a surface, such that the cyclic sequence of face degrees around each vertex is identical. In [1,4], semi-equivelar gems of PL d-manifolds embedded on surfaces with Euler characteristic χ≥ -1 were classified. In this paper, we extend this classification to semi-equivelar gems embedded on the double torus. We show that any such gem must belong to one of the following 31 types: (45), (64), (43,6), (43,8), (43,12), (42,62), (4,6,4,6), (42,82), (4,8,4,8), (83), (103), (62,8), (62,10), (62,12), (62,18), (102,4), (122,4), (162,4), (82,6), (122,6), (4,6,14), (4,6,16), (4,6,18), (4,6,20), (4,6,24), (4,6,36), (4,8,10), (4,8,12), (4,8,16), (4,8,24), and (4,10,20). Furthermore, we provide explicit constructions of semi-equivelar gems realizing each of these types.