University of Cambridge > Talks.cam > Geometric Group Theory (GGT) Seminar > Counting incompressible surfaces in 3-manifolds

Counting incompressible surfaces in 3-manifolds

Add to your list(s) Download to your calendar using vCal

  • UserNathan Dunfield (University of Illinois)
  • ClockFriday 14 February 2020, 13:45-14:45
  • HouseCMS, MR13.

If you have a question about this talk, please contact .

Counting embedded curves on a hyperbolic surface as a function of their length has been much studied by Mirzakhani and others. I will discuss analogous questions about counting incompressible surfaces in a hyperbolic 3-manifold, with the key difference that now the surfaces themselves have intrinsic topology. As there are only finitely many incompressible surfaces of bounded Euler characteristic up to isotopy in a hyperbolic 3-manifold, it makes sense to ask how the number of isotopy classes grows as a function of the Euler characteristic. Using Haken’s normal surface theory and facts about branched surfaces, we can characterize not just the rate of growth but show it is (essentially) a quasi-polynomial. Moreover, our method allows for explicit computations in reasonably complicated examples. This is joint work with Stavros Garoufalidis and Hyam Rubinstein.

This talk is part of the Geometric Group Theory (GGT) Seminar series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2020 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity