## Algebraic & Geometric Topology

### Knot exteriors with additive Heegaard genus and Morimoto's Conjecture

#### Abstract

Given integers $g≥2$, $n≥1$ we prove that there exist a collection of knots, denoted by $Kg,n$, fulfilling the following two conditions:

(1) For any integer $2≤h≤g$, there exist infinitely many knots $K∈Kg,n$ with $g(E(K))=h$.

(2) For any $m≤n$, and for any collection of knots $K1,…,Km∈Kg,n$, 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].

#### Article information

Source
Algebr. Geom. Topol., Volume 8, Number 2 (2008), 953-969.

Dates
Revised: 24 April 2008
Accepted: 28 April 2008
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513796852

Digital Object Identifier
doi:10.2140/agt.2008.8.953

Mathematical Reviews number (MathSciNet)
MR2443104

Zentralblatt MATH identifier
1149.57009

#### Citation

Kobayashi, Tsuyoshi; Rieck, Yo’av. Knot exteriors with additive Heegaard genus and Morimoto's Conjecture. Algebr. Geom. Topol. 8 (2008), no. 2, 953--969. doi:10.2140/agt.2008.8.953. https://projecteuclid.org/euclid.agt/1513796852

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