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We show that an infinite cyclic covering space M ′ of a PDn complex M is a PDn−1 -complex if and only if χ(M) = 0 and M ′ is homotopy equivalent to a complex with finite [(n − 1)/2]-skeleton and π1(M ) is finitely presentable. This is best possible in terms of minimal finiteness assumptions on the covering space. We give also a corresponding result for… (More)

We show that there are two homotopy types of PD3 -complexes with fundamental group S3 ∗Z/2Z S3 , and give explicit constructions for each, which differ only in the attachment of the top cell. AMS Classification 57P10; 55M05

The 2-knots with torsion-free, elementary amenable knot group and which have not yet been fully classified are fibred, with closed fibre the Hantzsche-Wendt flat 3-manifold HW or a Nil-manifold with base orbifold S(3, 3, 3). We give explicit normal forms for the strict weight orbits of normal generators for the groups of such knots, and determine when the… (More)

- JONATHAN A. HILLMAN, SWATEE NAIK
- 2005

Murasugi found two criteria that must be satisfied by the Alexander polynomial of a periodic knot. We generalize these to the case of twisted Alexander polynomials. Basic examples demonstrate the application of these new criteria. More delicate examples indicate their applicability to knots with trivial Alexander polynomial, including the two such knots… (More)

- J A Hillman, M Sakuma
- 2007

Let A be a nite abelian group and M be a branched cover of an homology 3-sphere, branched over a link L, with covering group A. We show that H 1 (M; Z1=jAj]) is determined as a Z1=jAj]]A]-module by the Alexander ideals of L and certain ideal class invariants. 1 ! be a-component link in an homology 3-sphere. The exterior of L is X(L) = ? N(L), where N(L) is… (More)

Given a knot and an SLnC representation of its group that is conjugate to its dual, the representation that replaces each matrix with its inverse-transpose, the associated twisted Reidemeister torsion is reciprocal. An example is given of a knot group and SL3Z representation that is not conjugate to its dual for which the twisted Reidemeister torsion is not… (More)

Let X be a PD4-complex with fundamental group π. We give conditions on the algebraic 2-type of X under which the homotopy type of X is determined by π, w = w1(X), the image of [X ] in H4(π; Z ) and the equivariant intersection pairing on π2(X). In particular, the homotopy type of an oriented Spin 4-manifold with fundamental group a PD2-group π is determined… (More)

- JILING CAO, IVAN L. REILLY, +4 authors Salvador Romaguera
- 1998

The aim of this paper is to explore some properties of quasiuniform multifunction spaces. Various kinds of completeness of the quasiuniform multifunction space .Y m X ;Um X / are characterized in terms of suitable properties of the range space .Y;U /. We also discuss the local compactness of quasiuniform multifunction spaces. By using the notion of… (More)

- J A Hillman, S K Roushon
- 2004

We show that although closed S̃L×En-manifolds do not admit metrics of nonpositive sectional curvature, the arguments of Farrell and Jones can be extended to show that such manifolds are topologically rigid, if n ≥ 2. 1 Smooth manifolds with Riemannian metrics of nonpositive curvature are topologically rigid, by the work of Farrell and Jones [3]. In [7] this… (More)

We give constraints on the Seifert invariants of orientable 3-manifolds which admit fixed-point free circle actions and embed in R. In particular, the generalized Euler invariant ε of the orbit fibration is determined up to sign by the base orbifold B unless H1(M ;Z) is torsion free, in which case it can take at most one nonzero value (up to sign). No such… (More)