Metabelian SL(n,C) representations of knot groups IV: twisted Alexander polynomials

In this paper we will study properties of twisted Alexander polynomials of knots corresponding to metabelian representations. In particular we answer a question of Wada about the twisted Alexander polynomial associated to the tensor product of two representations, and we settle several conjectures of Hirasawa and Murasugi

The SL(2,C) Casson invariant for Dehn surgeries on two-bridge knots

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 results of Ohtsuki, we outline how to compute the Culler--Shalen seminorms, and we illustrate this approach by providing explicit computations for double twist knots. We then apply the surgery formula of Curtis to deduce the SL(2,C) Casson invariant for the 3-manifolds obtained by p/q-Dehn surgery on such knots. These results are applied to prove nontriviality of the SL(2,C) Casson invariant for nearly all 3-manifolds obtained by nontrivial Dehn surgery on a hyperbolic two-bridge knot. We relate the formulas derived to degrees of A-polynomials and use this information to identify factors of higher multiplicity in the $\hat{A}$-polynomial, which is the A-polynomial with multiplicities as defined by Boyer-Zhang.Comment: 32 pages, 2 figures, to be published in Algebraic and Geometric Topolog

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 Poincar\'e polynomial is given.Comment: 25 pages, figure correcte

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.Comment: latex2

The Enemy Within: Homosexuality in the Third Reich, 1933-1945

From 1933 to 1945, the Nazi regime in Germany ruthlessly targeted homosexuals, particularly men, as enemies of the state. While Nazi doctrine officially repudiated same-sex romance, actual policy toward homosexuals in the Third Reich was by no means consistent. This paper examines the components of Nazi racial doctrines and the subtle ways in which the hyper-masculine ethos of the regime in fact encouraged male bonding and homosexual behavior. The differing views of prominent Nazi leaders on the issue of homosexuality are also discussed. The paper concludes by comparing the punishment of homosexual behavior among German soldiers in the Schutzstaffel (SS), and homosexuals unaffiliated with the Nazi party

OpTiX-II: A Software Environment for MCDM based on Distributed and Parallel Computing

The intention of the paper is to give an introduction to the OpTiX-II Software Environment, which supports the parallel and distributed solution of decision problems which can be represented as mathematical nonlinear programming tasks. First, a brief summary of nonsequential solution concepts for this class of decision problems on multiprocessor systems will be given. The focus of attention will be put on coarse-grained parallelization and its implementation on multi-computer clusters. The conceptual design objectives for the OpTiX-II Software Environment will be presented as well as the implementation on a workstation cluster, a transputer system and a multiprocessor workstation (shared memory). The OpTiX-II system supports the steps from the formulation of decision problems to their solution on networks of (parallel) computers. In order to demonstrate the use of OpTiX-II, the solution of a decision problem from the field of structural design is discussed and some numerical test results are supplied