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Topological Constructions in the o–Graph Calculus
Author(s) -
Theis Fabian J.
Publication year - 2002
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200207)241:1<170::aid-mana170>3.0.co;2-3
Subject(s) - mathematics , graph , puncturing , torus , topology (electrical circuits) , manifold (fluid mechanics) , discrete mathematics , combinatorics , calculus (dental) , geometry , mechanical engineering , statistics , engineering , medicine , dentistry
Benedetti and Petronio developed in [1] a so called o–Graph Calculus , where a compact oriented 3–manifold with nonempty boundary could be described by a quadrivalent graph together with some extra structure. In this paper, we will show how topological constructions such as puncturing, connected sums, attaching handles, closing boundary components and product and mapping tori constructions can be translated into the o–graph calculus.