New York Journal of Mathematics
Volume 26 (2020), 1130-1144


Ayse Borat

Higher dimensional simplicial complexity

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Published: October 1, 2020.
Keywords: Topological complexity, simplicial complexity, simplicial complex, barycentric subdivision, contiguous maps.
Subject: 05E45, 55M30, 57Q05.

In this paper we generalize the simplicial complexity, which is defined by Gonzalez in [5], to higher dimensions. We introduce some of its properties such as its relation with the topological complexity and the relation between the dimensions of the simplicial complexity. At the last section an example of a motion planner for a complex of S1 is given.


The author would like to thank Carlos Ortiz and Jesus Gonzalez for providing her the example in the last section. The author also thanks to the referees for their helpful comments and suggestions.

Author information

Ayse Borat:
Bursa Technical University
Faculty of Engineering and Natural Sciences
Department of Mathematics
Bursa, Turkey