Bridge spectra is a knot invariant first defined by Doll, who established some basic properties. Tomova has shown that high distance knots have bridge spectra $(n,n-1,\ldots,2,1,0)$. Zupan has computed the bridge spectra of iterated torus knots, which encompasses torus knots. Later Zupan, Bowman, and Taylor have looked into Bridge spectra of Twisted torus knots. Other than those few examples, does anyone know any classes of knots which have bridge spectra computed? Or know anyone who is working on computing a new class of knot's spectra? Thanks in advance for any responses.

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    $\begingroup$ Tomova's result holds for any knot for which the bridge number is the tunnel number $+1$. This holds, for example, for the 2-bridge knots, and 3-bridge knots which are not tunnel number 1, so e.g. not strongly invertible. $\endgroup$
    – Ian Agol
    Mar 31, 2015 at 3:41
  • $\begingroup$ @IanAgol Thank you, I was not aware of that. Do you know where I can find this result? If not, I can always ask her. $\endgroup$
    – N. Owad
    Mar 31, 2015 at 13:35
  • $\begingroup$ Have a look at the blog post: ldtopology.wordpress.com/2013/02/16/the-bridge-spectrum $\endgroup$
    – Ian Agol
    Mar 31, 2015 at 18:11


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