Three-manifolds with Heegaard genus at most two represented by crystallisations with at most 42 vertices

Autor:	Roman Nedela, Ján Karabáš, Peter Maličký
Rok vydání:	2007
Předmět:	Combinatorics Discrete mathematics Fundamental group Integer Discrete Mathematics and Combinatorics Tuple Graph Theoretical Computer Science Mathematics
Zdroj:	Discrete Mathematics. 307:2569-2590
ISSN:	0012-365X
DOI:	10.1016/j.disc.2006.11.017
Popis:	It is known that every closed compact orientable 3-manifold M can be represented by a 4-edge-coloured 4-valent graph called a crystallisation of M. Casali and Grasselli proved that 3-manifolds of Heegaard genus g can be represented by crystallisations with a very simple structure which can be described by a 2(g+1)-tuple of non-negative integers. The sum of first g+1 integers is called complexity of the admissible 2(g+1)-tuple. If c is the complexity then the number of vertices of the associated graph is 2c. In the present paper we describe all prime 3-manifolds of Heegaard genus two described by 6-tuples of complexity at most 21.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5d4db9da47449daee04a0637127081d2 https://doi.org/10.1016/j.disc.2006.11.017 Zobrazit plný text záznamu Full Text from ScienceDirect