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Now showing items 1-10 of 11

#### State invariants of 2-bridge knots

(World Scientific Publishing, 2018)

In this paper, we consider generalizations of the Alexander polynomial and signature of 2-bridge knots by considering the Gordon–Litherland bilinear forms associated with essential state surfaces of the 2-bridge knots. We ...

#### The Jones polynomial and boundary slopes of alternating Montesinos knots

(World Scientific Publishing, 2011)

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 maximal boundary slope of an essential ...

#### The SL(2,C) Casson invariant for knots and the Aˆ-polynomial

(Canadian Journal of Mathematics, 2016)

In this paper, we extend the definition of the SL(2, C) Casson invariant to arbitrary knots K in integral homology 3-spheres and relate it to the m-degree of the (A) over cap -polynomial of K. We prove a product formula ...

#### An intersection theory count of the -representations of the fundamental group of a 3-manifold

(Elsevier, 2001)

We define an invariant of closed 3-manifolds counting the signed equivalence classes of representations of the fundamental group in . The invariant is an -analog of the Casson-Walker invariant for SU(2). We reinterpret the ...

#### Generalized Casson Invariants for SO(3),U(2),Spin(4) , and SO(4)

(American Mathematical Society, 1994)

We investigate Casson-type invariants corresponding to the low-rank groups $\mathrm{SO}(3), \mathrm{SU}(2) \times S^1, \mathrm{U}(2), \operatorname{Spin}(4)$ and SO(4). The invariants are defined following an approach ...

#### A Dehn surgery description of regular finite cyclic covering spaces of rational homology spheres

(World Scientific Publishing, 2001)

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 descriptions to relate the Casson invariants of ...

#### A PSL(2,C) Casson Invariant

(American Mathematical Society, 2005)

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 note several properties of the invariant ...

#### Splicing and the SL(2,C) invariant

(American Mathematical Society, 2008)

We establish a formula for the SL2(C) Casson invariant of spliced sums of homology spheres along knots. Along the way, we show that the SL2(C) Casson invariant vanishes for spliced sums along knots in S-3.

#### Repeated boundary slopes for 2-bridge knots

(World Scientific Publishing, 2015)

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 instances in which this occurs and identify ...