Description

• Title:
  A classification of semi-equivelar gems of PL d-manifolds on the surface with Euler characteristic -1
• Creator:
  Agarwal, Anshu;
  Basak, Biplab
• Description:
  A semi-equivelar gem of a PL $d$-manifold is a regular colored graph that represents the PL $d$-manifold and regularly embeds on a surface, with the property that the cyclic sequence of lengths of faces in the embedding around each vertex is identical. In \cite{bb24}, the authors classified semi-equivelar gems of PL $d$-manifolds embedded on surfaces with Euler characteristics greater than or equal to zero. In this article, we focus on classifying semi-equivelar gems of PL $d$-manifolds embedded on the surface with Euler characteristic $-1$. We prove that if a semi-equivelar gem embeds regularly on the surface with Euler characteristic $-1$, then it belongs to one of the following types: $(8^3)$, $(6^2,8)$, $(6^2,12)$, $(10^2,4)$, $(12^2,4)$, $ (4,6,14)$, $(4,6,16)$, $(4,6,18)$, $(4,6,24)$, $(4,8,10)$, $(4,8,12)$ and $(4,8,16)$. Furthermore, we provide constructions that demonstrate the existence of such gems for each of the aforementioned types.
• Object availability:
  free access
• Date:
  2025.06.14
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Online First Articles; 1 - 20;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/62311/42823 ;https://apcz.umk.pl/TMNA/article/view/62311/42824
• Subject:
  Semi-equivelar maps;
  graph encoded manifold;
  semi-equivelar gems;
  regular embedding;
  Primary: 57Q15;
  Secondary: 05C15, 05C10, 52B70, 52C20
• Identifier: https://apcz.umk.pl/TMNA/article/view/62311
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other