New examples of tunnel number subadditivity
Trenton Schirmer
TL;DR
This paper constructs new examples of links that demonstrate the subadditivity of tunnel number, showing that the tunnel number of a connected sum can be less than the sum of individual tunnel numbers.
Contribution
The paper provides novel examples of subadditive links, advancing understanding of tunnel number behavior under connected sums.
Findings
New examples of subadditive links are constructed.
The results demonstrate that tunnel number can decrease under connected sum.
This work expands the known cases of tunnel number subadditivity.
Abstract
If the tunnel number of a link is denoted , a pair of knots is said to be subadditive if t(K_1)+t(K_2)>t(K_1 # K_2). We construct new examples of subadditive links.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Operator Algebra Research