We show that if f : M →M is a pseudo-Anosov homeomorphism on an orientable surface with oriented unstable manifolds and a quadratic expanding factor, then there is a hyperbolic toral automorphism on T2 and a map h : M → T2 such that h is a semi-conjugacy and (M, h) is a branched covering space of T2. We also give another characterization of pseudo-Anosov homeomorphisms with quadratic expansion ...

We give a form of the Van Kampen Theorem involving covering morphisms in a lextensive category. This includes the usual results for covering maps of locally connected spaces, for light maps of compact Hausdorff spaces, and for locally strong separable algebras. @ 1997 Elsevier Science B.V. 1991 Muth. Sut~j. Cluss.: lSB99,57MlO

We show that any 3–dimensional homotopy lens space M that is simplehomotopy equivalent to a lens space L(p, q) is topologically s-cobordant to the lens space. It follows that M has the same multi-signature as L(p, q) and the action of π1(M) on the universal cover of M embeds in a free orthogonal action on S . AMS Classification numbers Primary: 57M60, 57N70 Secondary: 57R65, 57R80

We use an algebraic description of surfaces with boundary to study covering maps. The focus is on the relationship between automor-phisms in the base and lifted maps. We show how to introduce and/or prohibit additional automorphisms in the lift. Using this control we give proofs of MacBeath's Theorem, Gr unbaum's Conjecture, and settle a conjecture of Nedela and Skoviera.

We introduce an algorithm for the automatic computation of global parameterizations on arbitrary simplicial 2manifolds, whose parameter lines are guided by a given frame field, for example, by principal curvature frames. The parameter lines are globally continuous and allow a remeshing of the surface into quadrilaterals. The algorithm converts a given frame field into a single vector field on a...

Let e ⊂ R be a finite union of disjoint closed intervals. We study measures whose essential support is e and whose discrete eigenvalues obey a 1/2-power condition. We show that a Szegő condition is equivalent to lim sup a1 · · · an cap(e) > 0 (this includes prior results of Widom and Peherstorfer–Yuditskii). Using Remling’s extension of the Denisov–Rakhmanov theorem and an analysis of Jost func...

This paper develops a formula for the equivariant chain-complex of the universal covering space of a Serre bration's total space in terms of equivariant chain-complexes of the base and ber. The present paper's distinguishing feature is that both the base and ber are allowed to be non-simply-connected: the fundamental group of the total space is thus an extension of that of the base by that of t...

We give an elementary construction of polyhedra whose links are connected bipartite graphs, which are not necessarily isomorphic pairwise. We show, that the fundamental groups of some of our polyhedra contain surface groups. In particular, we construct polyhedra whose links are generalized m-gons. The polyhedra of this type are interesting because of their universal coverings, which are two-dim...

No surgery on a non-torus 2-bridge knot yields a reducible 3-manifold as shown in Theorem 2(a) in [7] by A. Hatcher and W. Thurston. Dehn surgeries on 2-bridge knots are already well studied by M. Brittenham and Y.-Q. Wu in [2]. See also [11]. On 2-bridge links of 2-components, Wu showed in [13, Theorem 5.1 and Remark 5.5] the following theorem. The universal covering space of a laminar 3-manif...

In this paper we define the concept of a ramified covering map in the category of simplicial sets and we show that it has properties analogous to those of the topological ramified covering maps. We show that the geometric realization of a simplicial ramified covering map is a topological ramified covering map, and we also consider the relation with ramified covering maps in the category of simp...