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On Canonical Triangulations of Once-Punctured Torus Bundles and Two-bridge link complements

- François Guéritaud, D. Futer
- Mathematics
- 11 June 2004

We prove the hyperbolization theorem for punctured-torus bun- dles and two-bridge links by decomposing them into ideal tetrahedra which are then given hyperbolic structures.

88 12- PDF

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

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

The Jones polynomial and graphs on surfaces

- Oliver T. Dasbach, D. Futer, Efstratia Kalfagianni, X. Lin, N. Stoltzfus
- Computer Science, Mathematics
- J. Comb. Theory, Ser. B
- 21 May 2006

TLDR

121 2- 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

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

Ubiquitous quasi-Fuchsian surfaces in cusped hyperbolic 3-manifolds

This paper proves that every finite volume hyperbolic 3-manifold M contains a ubiquitous collection of closed, immersed, quasi-Fuchsian surfaces. These surfaces are ubiquitous in the sense that their… Expand

12 2- PDF

Explicit Dehn filling and Heegaard splittings

- D. Futer, J. Purcell
- Mathematics
- 16 April 2012

We prove an explicit, quantitative criterion that ensures the Heegaard surfaces in Dehn fillings behave "as expected." Given a cusped hyperbolic manifold X, and a Dehn filling whose meridian and… Expand

7 2- PDF

Finite surgeries on three-tangle pretzel knots

- D. Futer, M. Ishikawa, Y. Kabaya, T. Mattman, K. Shimokawa
- Mathematics
- 24 September 2008

We classify Dehn surgeries on (p, q, r) pretzel knots that result in a manifold of finite funda- mental group. The only hyperbolic pretzel knots that admit non-trivial finite surgeries are ( 2,3,7)… Expand

16 2- PDF

Dehn filling, volume, and the Jones polynomial

- D. Futer, Efstratia Kalfagianni, J. Purcell
- Mathematics
- 6 December 2006

Given a hyperbolic 3–manifold with torus boundary, we bound the change in volume under a Dehn filling where all slopes have length at least 2π. This result is applied to give explicit diagrammatic… Expand

99 1- PDF

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