Compact n-Manifolds via (n + 1)-Colored Graphs: a New Approach

• 来源期刊: 代数集刊（英文版）
• 关键词: compact manifolds colored graphs fundamental groups dipole moves
• 年，卷（期）: 2020,（1）
• 页码范围: 95-120
• 页数: 26页
• 语种: 英文
• DOI: 10.1142/S1005386720000097

摘要

We introduce a representation via (n + 1)-colored graphs of compact n-manifolds with (possibly empty) boundary,which appears to be very convenient for computer aided study and tabulation.Our construction is a generalization to arbitrary dimension of the one recently given by Cristofori and Mulazzani in dimension three,and it is dual to the one given by Pezzana in the 1970s.In this context we establish some results concerning the topology of the represented manifolds:suspensions,fundamental groups,connected sums and moves between graphs representing the same manifold.Classification results of compact orientable 4-manifolds representable by graphs up to six vertices are obtained,together with some properties of the G-degree of 5-colored graphs relating this approach to tensor models theory.