Strong Euler well-composedness

Nicolas Boutry (), Rocio Gonzalez-Diaz (), Maria-Jose Jimenez () and Eduardo Paluzo-Hildago ()
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Nicolas Boutry: EPITA Research and Development Laboratory (LRDE)
Rocio Gonzalez-Diaz: Universidad de Sevilla
Maria-Jose Jimenez: Universidad de Sevilla
Eduardo Paluzo-Hildago: Universidad de Sevilla

Journal of Combinatorial Optimization, 2022, vol. 44, issue 4, No 45, 3038-3055

Abstract: Abstract In this paper, we define a new flavour of well-composedness, called strong Euler well-composedness. In the general setting of regular cell complexes, a regular cell complex of dimension n is strongly Euler well-composed if the Euler characteristic of the link of each boundary cell is 1, which is the Euler characteristic of an $$(n-1)$$ ( n - 1 ) -dimensional ball. Working in the particular setting of cubical complexes canonically associated with $$n$$ n D pictures, we formally prove in this paper that strong Euler well-composedness implies digital well-composedness in any dimension $$n\ge 2$$ n ≥ 2 and that the converse is not true when $$n\ge 4$$ n ≥ 4 .

Keywords: Digital topology; Discrete geometry; Well-composedness; Cubical complexes; Manifolds; Euler characteristic (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10878-021-00837-8

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