WorldCat Identities

Kerckhoff, Steve

Overview
Works: 7 works in 9 publications in 1 language and 38 library holdings
Roles: Thesis advisor
Classifications: QA613.2, 514.3
Publication Timeline
Key
Publications about  Steve Kerckhoff Publications about Steve Kerckhoff
Publications by  Steve Kerckhoff Publications by Steve Kerckhoff
Most widely held works by Steve Kerckhoff
Three-dimensional orbifolds and cone-manifolds by Daryl Cooper ( Book )
2 editions published in 2000 in English and held by 28 WorldCat member libraries worldwide
The geometry and topology of three-manifolds by William P Thurston ( Book )
2 editions published in 1997 in English and held by 4 WorldCat member libraries worldwide
The geometry and topology of three-manifolds : lecture notes from Princeton University 1978-80 by William P Thurston ( Book )
in English and held by 2 WorldCat member libraries worldwide
Methods and applications of topological data analysis by Jennifer Novak Kloke ( )
1 edition published in 2010 in English and held by 1 WorldCat member library worldwide
The focus of this dissertation is the development of methods for topological analysis as well as the application of topological tools to real world problems. The first half of the dissertation focuses on an algorithm for de-noising high-dimensional data for topological data analysis. This method significantly extends the applicability of many topological data analysis methods. In particular, this method extends the use of persistent homology, a generalized notion of homology for discrete data points, to data sets that were previously inaccessible because of noise. The second half of this dissertation focuses on a method for using topology to simplify complex chemical structures and to define a metric to quantify similarity for use in screening large databases of chemical compounds. This method has shown very promising initial results in locating new materials for efficiently separating carbon dioxide from the exhaust of coal-burning power plants
Singular hyperbolic structures on pseudo-Anosov mapping tori by Kenji Kozai ( )
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
We study three-manifolds that are constructed as mapping tori of surfaces with pseudo-Anosov monodromy. We use Danciger's half-pipe geometry to regenerate hyperbolic structures when the monodromy has orientable foliations and its induced action on cohomology does not have 1 as an eigenvalue. We also include some discussion on Agol's veering triangulation construction
Geometric transitions from hyperbolic to Ads geometry by Jeffrey Edward Danciger ( )
1 edition published in 2011 in English and held by 1 WorldCat member library worldwide
We introduce a geometric transition between two homogeneous three-dimensional geometries: hyperbolic geometry and anti de Sitter (AdS) geometry. Given a path of three-dimensional hyperbolic structures that collapse down onto a hyperbolic plane, we describe a method for constructing a natural continuation of this path into AdS structures. In particular, when hyperbolic cone manifolds collapse, the AdS manifolds generated on the "other side" of the transition have tachyon singularities. The method involves the study of a new transitional geometry called half-pipe geometry. We also discuss combinatorial/algebraic tools for constructing transitions using ideal tetrahedra. Using these tools we prove that transitions can always be constructed when the underlying manifold is a punctured torus bundle
String topology and the based loop space by Eric James Malm ( )
1 edition published in 2010 in English and held by 1 WorldCat member library worldwide
We relate the Batalin-Vilkovisky (BV) algebra structure of the string topology of a manifold to the homological algebra of the singular chains of the based loop space of that manifold, showing that its Hochschild cohomology carries a BV algebra structure isomorphic to that of string topology. Furthermore, this structure is compatible with the usual cup product and Lie bracket on Hochschild cohomology. This isomorphism arises from a derived form of Poincare duality using modules over the based loop space as local coefficient systems. This derived Poincare duality also comes from a form of fibrewise Atiyah duality on the level of fibrewise spectra, and we use this perspective to connect the algebraic constructions to the Chas-Sullivan loop product
 
Audience Level
0
Audience Level
1
  Kids General Special  
Audience level: 0.89 (from 0.47 for Geometric ... to 0.96 for Three-dime ...)
Alternative Names
Kerckhoff, Steven P.
Languages
English (9)