On the crystallization of 3-manifolds associated with polyhedral schemata

Kyung-Hee Ko; Hyun-Jong Song

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 1999; 36(3): 447-458

Printed May 1, 1999

On the crystallization of 3-manifolds associated with polyhedral schemata

Kyung-Hee Ko and Hyun-Jong Song

Abstract

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Abstract

In this paper we introduce a method of presenting 3-manifolds by polyhedral schemata with 2 vertices so that they may be naturally associated with given crystallizations of 3-manifolds. As applications, we explicitly present crystallizations of $n$-fold cyclic branched coverings of $S^3$ over 2-bridge knots.

Keywords: crystallizations, polyhedral schemata, Heegaard diagrams, cyclic branched coverings, 2-bridge knots

MSC numbers: Primary 57M12, 57M15; Secondary 05C10, 05C15