arXiv subjects

H. U. Boden

Publications and source records attributed to H. U. Boden.

4 recordsLinked to original sources

arXiv2002

Invariants of fibred knots from moduli

An invariant $μ_α(K)$ of fibred knots $K$ in a homology sphere is defined for each $α\in {\bold S}{\bold U}_n$ as follows. Since the knot is fibred, the knot complement is described by an element of the mapping class group, which induces an action on the variety of ${\bold S}{\bold U}_n$ representations of the surface group. Restricting attention to those representations with holonomy along the longitude conjugate to $a \in {\bold S}{\bold U}_n,$ one can define $μ_α(K)$ to be the Lefschetz number of this action. The dependence of $μ_α(K)$ on $α$ is studied and formulas relating $μ_α(K)$ to $μ_β(K)$ are derived for $α,β\in ${\bold S}{\bold U}_n$.$

q-alg↗

arXiv1998

Moduli Spaces of Parabolic Higgs Bundles and Parabolic K(D) Pairs over Smooth Curves: I

This paper concerns the moduli spaces of rank two parabolic Higgs bundles and parabolic K(D) pairs over a smooth curve. Precisely which parabolic bundles occur in stable K(D), pairs and stable Higgs bundles is determined. Using Morse theory, the moduli space of parabolic Higgs bundles is shown to be a non-compact, connected, simply connected manifold, and a computation of its Poincaré polynomial is given.

alg-geom↗

arXiv1996

Integrality of the Averaged Jones Polynomial of Algebraically Split Links

X.-S. Lin and Z. Wang recently made a conjecture concerning the integrality of the Taylor coefficients of the averaged Jones polynomial of algebraically split links. This question is related to a conjectural integrality result for the Ohtsuki invariants, which are rational topological invariants of homology 3-spheres derived from the quantum invariants of Witten and Reshetikhin-Turaev. This paper presents counterexamples to the conjecture of Lin and Wang and gives a proof of a corrected statement of the conjecture. The statement is divided into two parts. The first part applies to geometrically split links and gives an integrality result which is stronger than conjectured, while the second is valid for any algebraically split link and gives a somewhat weaker statement. Both propositions are seen to be sharp by the examples given.

q-alg↗

arXiv1996

Rationality of Moduli Spaces of Parabolic Bundles

The moduli space of parabolic bundles with fixed determinant over a smooth curve of genus greater than one is proved to be rational whenever one of the multiplicities associated to the quasi-parabolic structure is equal to one. It follows that if rank and degree are coprime, the moduli space of vector bundles is stably rational, and the bound obtained on the level is strong enough to conclude rationality in many cases.

alg-geom↗