Results 1 
7 of
7
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. ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
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.
A PREHISTORY OF nCATEGORICAL PHYSICS
, 2008
"... We begin with a chronology tracing the rise of symmetry concepts in physics, starting with groups and their role in relativity, and leading up to more sophisticated concepts from ncategory theory, which manifest themselves in Feynman diagrams and their higherdimensional generalizations: strings, me ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
We begin with a chronology tracing the rise of symmetry concepts in physics, starting with groups and their role in relativity, and leading up to more sophisticated concepts from ncategory theory, which manifest themselves in Feynman diagrams and their higherdimensional generalizations: strings, membranes and spin foams.
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 ..."
Abstract
 Add to MetaCart
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
4Manifolds with a Symplectic Bias
"... Abstract. This text reviews some state of the art and open questions on (smooth) 4manifolds from the point of view of symplectic geometry. ..."
Abstract
 Add to MetaCart
Abstract. This text reviews some state of the art and open questions on (smooth) 4manifolds from the point of view of symplectic geometry.
Global Existence for the SeibergWitten Flow
, 2009
"... Abstract. We introduce the gradient flow of the SeibergWitten functional on a compact, orientable Riemannian 4manifold and show the global existence of a unique smooth solution to the flow. The flow converges uniquely in C ∞ up to gauge to a critical point of the SeibergWitten functional. 1 ..."
Abstract
 Add to MetaCart
Abstract. We introduce the gradient flow of the SeibergWitten functional on a compact, orientable Riemannian 4manifold and show the global existence of a unique smooth solution to the flow. The flow converges uniquely in C ∞ up to gauge to a critical point of the SeibergWitten functional. 1
An Introduction to Exotic 4manifolds
, 812
"... This article intends to provide an introduction to the ..."