[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2015.55.4.753

Characteristic Genera of Closed Orientable 3-Manifolds

KAWAUCHI, AKIO (Osaka City University Advanced Mathematical Institute)

Publication Information

Kyungpook Mathematical Journal / v.55, no.4, 2015 , pp. 753-771 More about this Journal

Abstract

A complete invariant defined for (closed connected orientable) 3-manifolds is an invariant defined for the 3-manifolds such that any two 3-manifolds with the same invariant are homeomorphic. Further, if the 3-manifold itself can be reconstructed from the data of the complete invariant, then it is called a characteristic invariant defined for the 3-manifolds. In a previous work, a characteristic lattice point invariant defined for the 3-manifolds was constructed by using an embedding of the prime links into the set of lattice points. In this paper, a characteristic rational invariant defined for the 3-manifolds called the characteristic genus defined for the 3-manifolds is constructed by using an embedding of a set of lattice points called the PDelta set into the set of rational numbers. The characteristic genus defined for the 3-manifolds is also compared with the Heegaard genus, the bridge genus and the braid genus defined for the 3-manifolds. By using this characteristic rational invariant defined for the 3-manifolds, a smooth real function with the definition interval (-1, 1) called the characteristic genus function is constructed as a characteristic invariant defined for the 3-manifolds.

Keywords

Braid; 3-manifold; Prime link; Characteristic genus; Characteristic function;

Citations & Related Records

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