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Branched coverings, open books and knot periodicity
 Topology
, 1974
"... THIS paper generalizes some properties of hypersurface singularities into the combined contexts of branched covering spaces and open book decompositions. Perhaps the most striking corollary of this analysis is a completely topological construction ofthe Brieskorn manifolds C(a, ,..., a,) = V(f) n S ..."
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THIS paper generalizes some properties of hypersurface singularities into the combined contexts of branched covering spaces and open book decompositions. Perhaps the most striking corollary of this analysis is a completely topological construction ofthe Brieskorn manifolds C(a, ,..., a,) = V(f) n S’“+l (forf=zOso f.. * + z,““, zi
A wild knot S 2 ֒ → S 4 as limit set of a Kleinian Group: Indra’s pearls in four dimensions.
, 2003
"... The purpose of this paper is to construct an example of a 2knot wildly embedded in S 4 as the limit set of a Kleinian group. We find that this type of wild 2knots has very interesting topological properties. 1 ..."
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The purpose of this paper is to construct an example of a 2knot wildly embedded in S 4 as the limit set of a Kleinian group. We find that this type of wild 2knots has very interesting topological properties. 1
BETWEEN LOWER AND HIGHER DIMENSIONS (in the work of Terry Lawson)
"... There are several approaches to summarizing a mathematician’s research accomplishments, and each has its advantages and disadvantages. This article is based upon a talk given at Tulane that was aimed at a fairly general audience, including faculty members in other areas and graduate students who had ..."
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There are several approaches to summarizing a mathematician’s research accomplishments, and each has its advantages and disadvantages. This article is based upon a talk given at Tulane that was aimed at a fairly general audience, including faculty members in other areas and graduate students who had taken the usual entry level courses. As such, it is meant to be relatively nontechnical and to emphasize qualitative rather than quantitative issues; in keeping with this aim, references will be given for some standard topological notions that are not normally treated in entry level graduate courses. Since this was an hour talk, it was also not feasible to describe every single piece of published mathematical work that Terry Lawson has ever written; in particular, some papers like [42] and [50] would require lengthy digressions that are not easily related to the central themes in his main lines of research. Instead, we shall focus on some ways in which Terry’s work relates to an important thread in geometric topology; namely, the passage from studying problems in a given dimension to studying problems in the next dimensions. Qualitatively speaking, there are fairly welldeveloped theories for very low dimensions and for all sufficiently large dimensions, but between these ranges there are some dimensions in which the answers to many fundamental
Wild Knots as limit sets of Kleinian Groups ∗
, 2004
"... Dedicated to Alberto Verjovsky on the occasion of his 60 th anniversary. In this paper we study kleinian groups of Schottky type whose limit set is a wild knot in the sense of Artin and Fox. We show that, if the “original knot ” fibers over the circle then the wild knot Λ also fibers over the circle ..."
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Dedicated to Alberto Verjovsky on the occasion of his 60 th anniversary. In this paper we study kleinian groups of Schottky type whose limit set is a wild knot in the sense of Artin and Fox. We show that, if the “original knot ” fibers over the circle then the wild knot Λ also fibers over the circle. As a consequence, the universal covering of S 3 − Λ is R 3. We prove that the complement of a dynamicallydefined fibered wild knot can not be a complete hyperbolic 3manifold. 1
WILD KNOTS IN HIGHER DIMENSIONS AS LIMIT SETS OF KLEINIAN GROUPS
"... Abstract. In this paper we construct infinitely many wild knots, S n ↩ → S n+2, for n =1, 2, 3, 4 and 5, each of which is a limit set of a geometrically finite Kleinian group. We also describe some of their properties. 1. ..."
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Abstract. In this paper we construct infinitely many wild knots, S n ↩ → S n+2, for n =1, 2, 3, 4 and 5, each of which is a limit set of a geometrically finite Kleinian group. We also describe some of their properties. 1.
Regularization of Γ1structures in dimension 3
, 2009
"... Abstract. For Γ1structures on 3manifolds, we give a very simple proof of Thurston’s regularization theorem, first proved in [13], without using Mather’s homology equivalence. Moreover, in the coorientable case, the resulting foliation can be chosen of a precise kind, namely an “open book foliatio ..."
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Abstract. For Γ1structures on 3manifolds, we give a very simple proof of Thurston’s regularization theorem, first proved in [13], without using Mather’s homology equivalence. Moreover, in the coorientable case, the resulting foliation can be chosen of a precise kind, namely an “open book foliation modified by suspension”. There is also a model in the non coorientable case.