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Equilibrium decompositions of 4‐manifolds and abstract regular 5‐polytopes
Author(s) -
Kühnel Wolfgang
Publication year - 1997
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300012006
Subject(s) - mathematics , polytope , genus , combinatorics , intersection (aeronautics) , type (biology) , manifold (fluid mechanics) , surface (topology) , point (geometry) , pure mathematics , geometry , paleontology , botany , mechanical engineering , engineering , biology , aerospace engineering
Decompositions of simply connected 4‐manifolds into three closed 4‐balls are studied from the view‐point of abstract regular polytopes of Schläfli type { p, q , 2, 3}. The three balls correspond to three ditopes, their common intersection corresponds to a regular map of type { p, q } as an equilibrium surface whose genus equals the “genus” of the 4‐manifold.