17 citations · 38 across the 9 of their papers we have counts for
10 papers
Weights of essential surfaces in 2-bridge knot complements
Cynthia L. Curtis, Kendra Ebke, Kate O'Connor
Understanding ideal points in the character varieties of knot complements has led to a number of important invariants for 3-manifolds. Ohtsuki (1994) counted the ideal points for c…
State invariants of two-bridge knots
Cynthia L. Curtis, Vincent Longo
In this paper, we consider generalizations of the Alexander polynomial and signature of 2-bridge knots by considering the Gordon-Litherland bilinear forms associated to essential s…
Repeated boundary slopes for 2-bridge knots
Cynthia L. Curtis, William Franczak, Randolph J. Leiser +1
We investigate the question of when distinct branched surfaces in the complement of a 2-bridge knot support essential surfaces with identical boundary slopes. We determine all inst…
The SL(2,C) Casson invariant for knots and the -polynomial
Hans U. Boden, Cynthia L. Curtis
In this paper, we extend the definition of the Casson invariant to arbitrary knots in integral homology 3-spheres and relate it to the -degree of the $\wideha…
The SL(2,C) Casson invariant for Dehn surgeries on two-bridge knots
Hans U. Boden, Cynthia L. Curtis
We investigate the behavior of the SL(2,C) Casson invariant for 3-manifolds obtained by Dehn surgery along two-bridge knots. Using the results of Hatcher and Thurston, and also res…
The Jones polynomial and boundary slopes of alternating knots
Cynthia L. Curtis, Samuel Taylor
We show for an alternating knot the minimal boundary slope of an essential spanning surface is given by the signature plus twice the minimum degree of the Jones polynomial and the…
Splicing and the SL(2,C) Casson invariant
Hans U. Boden, Cynthia L. Curtis
We establish a formula for the SL(2,C) Casson invariant of spliced sums of homology spheres along knots. Along the way, we show that the SL(2,C) Casson invariant vanishes for splic…
The SL(2,C) Casson invariant for Seifert fibered homology spheres and surgeries on twist knots
Hans U. Boden, Cynthia L. Curtis
We derive a simple closed formula for the SL(2,C) Casson invariant for Seifert fibered homology 3-spheres using the correspondence between SL(2,C) character varieties and moduli sp…
A PSL(2,C) Casson Invariant
Cynthia L. Curtis
We use intersection theory techniques to define an invariant of closed 3-manifolds counting the characters of irreducible representations of the fundamental group in PSL(2,C). We n…
A Dehn surgery description of regular finite cyclic covering spaces of rational homology spheres
Cynthia L. Curtis
We provide related Dehn surgery descriptions for rational homology spheres and a class of their regular finite cyclic covering spaces. As an application, we use the surgery descrip…