Authors: Timotijević, Marinko
Živaljević, Rade 
Affiliations: Mechanics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Constructing self-dual complexes and self-dual triangulations of manifolds
Journal: Filomat
Volume: 38
Issue: 5
First page: 2045
Last page: 2060
Issue Date: 1-Jan-2024
Rank: ~M22
ISSN: 0354-5180
DOI: 10.2298/FIL2406045T
Abstract: 
Simplicial complexes K, which are equal to their Alexander dual KΛ are known as self-dual simplicial complexes. We prove that topological and combinatorial properties of any self-dual simplicial complex, are fully determined by topological and combinatorial properties of the link of any of it’s vertices which happens to be sub-dual in smaller combinatorial ambient. Using this observation, we describe a general method for constructing self-dual triangulations of given topological spaces and focus on self-dual triangulations of compact manifolds. We show that there exist only 4 types of self-dual combinatorial manifolds and provide a general method for their construction.
Keywords: Brehm and Kühnel triangulations | combinatorial Alexander dual | combinatorial manifold | manifold like a projective plane | octonionic projective plane | Self-dual complex
Publisher: University of Niš : Faculty of Sciences and Mathematics, Serbia

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