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Guts of Surfaces and the Colored Jones Polynomial

- D. Futer, Efstratia Kalfagianni, J. Purcell
- Mathematics, Computer Science
- Lecture notes in mathematics
- 16 August 2011

TLDR

64 10- PDF

Geometrically and diagrammatically maximal knots

- Abhijit Champanerkar, I. Kofman, J. Purcell
- Mathematics, Computer Science
- J. Lond. Math. Soc.
- 28 November 2014

TLDR

28 9- PDF

An introduction to fully augmented links

- J. Purcell
- Mathematics
- 2011

In this article we summarize information on the class of fully augmented links. These links are geometrically explicit, and therefore provide a large class of examples of hyperbolic links for which… Expand

35 9- PDF

Links with no exceptional surgeries

- D. Futer, J. Purcell
- Mathematics
- 15 December 2004

We show that if a knot admits a prime, twist-reduced diagram with at least 4 twist regions and at least 6 crossings per twist region, then every non-trivial Dehn filling of that knot is hyperbolike.… Expand

44 6- PDF

Geometry of alternating links on surfaces.

- J. Howie, J. Purcell
- Mathematics
- 4 December 2017

We consider links that are alternating on surfaces embedded in a compact 3-manifold. We show that under mild restrictions, the complement of the link decomposes into simpler pieces, generalising the… Expand

17 5- PDF

Geometry of biperiodic alternating links

- Abhijit Champanerkar, I. Kofman, J. Purcell
- Mathematics, Computer Science
- J. Lond. Math. Soc.
- 14 February 2018

TLDR

19 5- PDF

The length of unknotting tunnels

- D. Cooper, M. Lackenby, J. Purcell
- Mathematics
- 4 December 2008

We show there exist tunnel number one hyperbolic 3-manifolds with arbitrarily long unknotting tunnel. This provides a negative answer to an old question of Colin Adams.

10 3- PDF

Cusp Areas of Farey Manifolds and Applications to Knot Theory

- D. Futer, Efstratia Kalfagianni, J. Purcell
- Mathematics
- 20 August 2008

This paper gives the first explicit, two-sided estimates on the cusp area of once-punctured-torus bundles, 4-punctured sphere bundles, and two-bridge link complements. The input for these estimates… Expand

30 2- PDF

Volume bounds for weaving knots

- Abhijit Champanerkar, I. Kofman, J. Purcell
- Mathematics
- 10 June 2015

Weaving knots are alternating knots with the same projection as torus knots, and were conjectured by X.-S. Lin to be among the maximum volume knots for fixed crossing number. We provide the first… Expand

21 2- PDF

Quasifuchsian state surfaces

- D. Futer, Efstratia Kalfagianni, J. Purcell
- Mathematics
- 25 September 2012

This paper continues our study, initiated in [arXiv:1108.3370], of essential state surfaces in link complements that satisfy a mild diagrammatic hypothesis (homogeneously adequate). For hyperbolic… Expand

22 2- PDF

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