Futer and Atkinson to speak at the Spring 2011 AMS Eastern Sectional Meeting

Chris Atkinson and Dave Futer will be speaking at the AMS Eastern Sectional Meeting.

Futer will be giving two talks:

Title: Slopes and colored Jones polynomials of adequate knots

Abstract: Garoufalidis conjectured a relation between the boundary slopes of a knot and its colored Jones polynomials. According to the conjecture, certain boundary slopes are detected by the sequence of degrees of the colored Jones polynomials. We prove this conjecture for adequate knots, a class that vastly generalizes that of alternating knots.

Title: The geometry of unknotting tunnels

Abstract: Given a 3-manifold M, with boundary a union of tori, an unknotting tunnel for M is an arc from the boundary back to the boundary, such that the complement of  in M is a genus-2 handlebody. Fifteen years ago, Colin Adams asked a series of questions about how the topological data of an unknotting tunnel fi ts into the hyperbolic structure on M. For
example: is  isotopic to a geodesic? Can it be arbitrarily long, relative to a maximal cusp neighborhood? Does  appear as an edge in the canonical polyhedral decomposition?

Although the most general versions of these questions are still open today, I will describe fairly complete answers in the case where M is created by a “generic” Dehn fi lling. As an application, there is an explicit family of knots in S^3
whose tunnels are arbitrarily long. This is joint work with Daryl Cooper and Jessica Purcell.

Atkinson will speak on:

Title: Geometry and topology of polyhedral 3-orbifolds

Abstract: We will describe the geometric decomposition of polyhedral 3{orbifolds. We will show how this decomposition can be detected algorithmically and how it can be applied to yield lower volume bounds for hyperbolic polyhedral orbifolds.

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