41 citations · 113 across the 16 of their papers we have counts for
16 papers
A differential topology proof that the character variety of the genus two surface is homeomorphic to
Christopher M. Herald, Paul Kirk
We provide a proof that the character variety of a genus two surface, , is a closed compact manifold, and a proof of the Narasimhan-Ramanan theorem that is…
An endomorphism on immersed curves in the pillowcase
Christopher M. Herald, Paul Kirk
We examine the holonomy-perturbed traceless SU(2) character variety of the trivial four-stranded tangle {p_1,p_2,p_3,p_4} X [0,1] in S^2 X [0,1] equipped with a strong marking, eit…
Examples of homology 3-spheres whose Chern-Simons function is not Morse-Bott
Hans U Boden, Christopher Herald, Paul Kirk
We construct two homology 3-spheres for which the (unperturbed) Chern-Simons function is not Morse-Bott. In one case, there is a degenerate isolated critical point. In the…
Tangles, relative character varieties, and holonomy perturbed traceless flat moduli spaces
Guillem Cazassus, Chris Herald, Paul Kirk
We prove that the restriction map from the subspace of regular points of the holonomy perturbed SU(2) traceless flat moduli space of a tangle in a 3-manifold to the traceless flat…
The correspondence induced on the pillowcase by the earring tangle
Guillem Cazassus, Christopher M. Herald, Paul Kirk +1
The earring tangle consists of four strands 4pt x [0,1] inside S^2 x [0,1] and one meridian around one of the strands. Equipping this tangle with a nontrivial SO(3) bundle, we show…
The Fukaya category of the pillowcase, traceless character varieties, and Khovanov Cohomology
Matthew Hedden, Christopher M. Herald, Matthew Hogancamp +1
For a diagram of a 2-stranded tangle in the 3-ball we define a twisted complex of compact Lagrangians in the triangulated envelope of the Fukaya category of the smooth locus of the…
The SU(2) Casson-Lin invariant of the Hopf link
Hans U. Boden, Christopher M. Herald
We compute the Casson-Lin invariant for the Hopf link and determine the sign in the formula of Harper and Saveliev relating this invariant to the linking number.
Holonomy perturbations in a cylinder, and regularity for traceless SU(2) character varieties of tangles
Christopher M. Herald, Paul Kirk
The traceless character variety of a -punctured 2-sphere is the symplectic reduction of a Hamiltonian -torus action on the chara…
The pillowcase and traceless representations of knot groups II: a Lagrangian-Floer theory in the pillowcase
Matthew Hedden, Christopher M. Herald, Paul Kirk
We define an elementary relatively graded Lagrangian-Floer chain complex for restricted immersions of compact 1-manifolds into the pillowcase, and apply it to the int…
The pillowcase and perturbations of traceless representations of knot groups
Matthew Hedden, Chris Herald, Paul Kirk
We introduce explicit holonomy perturbations of the Chern-Simons functional on a 3-ball containing a pair of unknotted arcs. These perturbations give us a concrete local method for…
Metabelian representations, twisted Alexander polynomials, knot slicing, and mutation
Chris Herald, Paul Kirk, Charles Livingston
Given a knot complement X and its p-fold cyclic cover X_p, we identify twisted polynomials associated to 1-dimensional linear representations of the fundamental group of X_p with t…
The Integer Valued SU(3) Casson Invariant for Brieskorn spheres
Hans U. Boden, Christopher M. Herald, Paul A. Kirk
We develop techniques for computing the integer valued SU(3) Casson invariant. Our method involves resolving the singularities in the flat moduli space using a twisting perturbatio…
An integer valued SU(3) Casson invariant
Hans U. Boden, Christopher M. Herald, Paul A. Kirk
We define an integer valued invariant of homology spheres using the methods of SU(3) gauge theory and study its behavior under orientation reversal and connected sum.
A connected sum formula for the SU(3) Casson invariant
Hans U. Boden, Christopher M. Herald
We provide a formula for the SU(3) Casson invariant for 3-manifolds given as the connected sum of two integral homology 3-spheres.
Gauge Theoretic Invariants of, Dehn Surgeries on Knots
Hans U Boden, Christopher M Herald, Paul A Kirk +1
New methods for computing a variety of gauge theoretic invariants for homology 3-spheres are developed. These invariants include the Chern-Simons invariants, the spectral flow of t…
The SU(3) Casson Invariant for Integral Homology 3-Spheres
Hans U. Boden, Christopher M. Herald
We derive a gauge theoretic invariant of integral homology 3-spheres which counts gauge orbits of irreducible, perturbed flat SU(3) connections with sign given by spectral flow. To…