# New examples of tunnel number subadditivity

@inproceedings{Schirmer2011NewEO, title={New examples of tunnel number subadditivity}, author={Trenton Frederick Schirmer}, year={2011} }

Abstract If the tunnel number of a knot K is denoted t ( K ) , a pair of knots K 1 , K 2 is said to be subadditive if t ( K 1 ) + t ( K 2 ) > t ( K 1 # K 2 ) . Scharlemann and Schultens (2000) [11] defined the degeneration ratio to be d ( K 1 , K 2 ) = 1 − t ( K 1 # K 2 ) t ( K 1 ) + t ( K 2 ) , and proved that d ( K 1 , K 2 ) ⩽ 3 / 5 . However, the highest known degeneration ratio known for a pair of knots is just 2/5. We use free decompositions to construct links which experience degeneration… CONTINUE READING

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