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Now showing items 1-10 of 26

#### 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 ...

#### The SL(2,C) Casson invariant for Seifert fibered homology spheres and surgeries on twist knots

(World Scientific Publishing, 2006)

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 spaces of parabolic Higgs bundles of rank ...

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

(2011-04)

We show for an alternating knot the minimal integral boundary slope is given by the signature plus twice the minimum degree of the Jones polynomial and the maximal integral boundary slope is given by the signature plus ...

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

(2009-10-22)

The boundary slopes of essential surfaces in the complement of a knot have been a valuable tool in the study of the knot. These slopes play a key role in the definitions of the A-polynomial of the knot and of the ...

#### The SL(2,C) Casson invariant for Dehn surgery on 2-bridge knots

(2014-07)

Recent study of the properties of 3-manifolds obtained by Dehn surgery on a given knot has often involved knot invariants coming from the character variety of the knot complement. We investigate the behavior of the SL(2,C) ...