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2008 Knot exteriors with additive Heegaard genus and Morimoto's Conjecture
Tsuyoshi Kobayashi, Yo’av Rieck
Algebr. Geom. Topol. 8(2): 953-969 (2008). DOI: 10.2140/agt.2008.8.953

Abstract

Given integers g2, n1 we prove that there exist a collection of knots, denoted by Kg,n, fulfilling the following two conditions:

(1) For any integer 2hg, there exist infinitely many knots KKg,n with g(E(K))=h.

(2) For any mn, and for any collection of knots K1,,KmKg,n, the Heegaard genus is additive:

g ( E ( # i = 1 m K i ) ) = i = 1 m g ( E ( K i ) ) .

This implies the existence of counterexamples to Morimoto’s Conjecture [Math. Ann. 317 (2000) 489–508].

Citation

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Tsuyoshi Kobayashi. Yo’av Rieck. "Knot exteriors with additive Heegaard genus and Morimoto's Conjecture." Algebr. Geom. Topol. 8 (2) 953 - 969, 2008. https://doi.org/10.2140/agt.2008.8.953

Information

Received: 1 May 2007; Revised: 24 April 2008; Accepted: 28 April 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1149.57009
MathSciNet: MR2443104
Digital Object Identifier: 10.2140/agt.2008.8.953

Subjects:
Primary: 57M25
Secondary: 57M27

Rights: Copyright © 2008 Mathematical Sciences Publishers

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