Heegaard genus of the connected sum of m-small knots

2005/03/12 by Kobayashi, Tsuyoshi, Rieck, Yo'av
#57M25 #57M99 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.math/0503229

Abstract

We prove that if K₁ ⊂ M₁,...,K_n ⊂ M_n are m-small knots in closed orientable 3-manifolds then the Heegaard genus of E(#_i=1ⁿ K_i) is strictly less than the sum of the Heegaard genera of the E(K_i) (i=1,...,n) if and only if there exists a proper subset I of \1,...,n\ so that #_{i ∈ I} K_i admits a primitive meridian. This generalizes the main result of Morimoto in \citemorimoto1.

Related

• Morimoto's Conjecture for m-small knots
• Heegaard genus, degree-one maps, and amalgamation of 3-manifolds
• Small Heegaard genus and SU(2)
• Small knots of large Heegaard genus
• Knot exteriors with additive Heegaard genus and Morimoto's Conjecture