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Detecting codimension one manifold factors with 0stitched disks
 Topology Appl
, 2007
"... Abstract. We prove recognition theorems for codimension one manifold factors of dimension n ≥ 4. In particular, we formalize topographical methods and introduce three ribbons properties: the crinkled ribbons property, the twisted crinkled ribbons property, and the fuzzy ribbons property. We show tha ..."
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Abstract. We prove recognition theorems for codimension one manifold factors of dimension n ≥ 4. In particular, we formalize topographical methods and introduce three ribbons properties: the crinkled ribbons property, the twisted crinkled ribbons property, and the fuzzy ribbons property. We show that X × R is a manifold in the cases when X is a resolvable generalized manifold of finite dimension n ≥ 3 with either: (1) the crinkled ribbons property; (2) the twisted crinkled ribbons property and the disjoint point disk property; or (3) the fuzzy ribbons property. 1.
THE BINGBORSUK AND THE BUSEMANN CONJECTURES
, 811
"... Abstract. We present two classical conjectures concerning the characterization of manifolds: the Bing Borsuk Conjecture asserts that every ndimensional homogeneous ANR is a topological nmanifold, whereas the Busemann Conjecture asserts that every ndimensional Gspace is a topological nmanifold. ..."
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Abstract. We present two classical conjectures concerning the characterization of manifolds: the Bing Borsuk Conjecture asserts that every ndimensional homogeneous ANR is a topological nmanifold, whereas the Busemann Conjecture asserts that every ndimensional Gspace is a topological nmanifold. The key object in both cases are socalled generalized manifolds, i.e. ENR homology manifolds. We look at the history, from the early beginnings to the present day. We also list several open problems and related conjectures. 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
PROBLEMS ON HOMOLOGY MANIFOLDS
, 2003
"... Abstract. A compilation for the proceedings of the Workshop on Exotic Homology ..."
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Abstract. A compilation for the proceedings of the Workshop on Exotic Homology
CONSTRUCTING NEAREMBEDDINGS OF CODIMENSION ONE MANIFOLDS WITH COUNTABLE DENSE SINGULAR SETS
, 803
"... Abstract. The purpose of this paper is to present, for all n ≥ 3, very simple examples of continuous maps f: M n−1 → M n from closed (n − 1)manifolds M n−1 into closed nmanifold M n such that even though the singular set S(f) of f is countable and dense, the map f can nevertheless be approximated ..."
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Abstract. The purpose of this paper is to present, for all n ≥ 3, very simple examples of continuous maps f: M n−1 → M n from closed (n − 1)manifolds M n−1 into closed nmanifold M n such that even though the singular set S(f) of f is countable and dense, the map f can nevertheless be approximated by an embedding, i.e. f is a nearembedding. Notice that in such case in dimension 3 one can get even a piecewiselinear approximation by an embedding [2]. 1.