Format: Paperback

Language: English

Format: PDF / Kindle / ePub

Size: 6.04 MB

Downloadable formats: PDF

Pages: 238

Publisher: Cambridge University Press; 1 edition (May 28, 2001)

ISBN: 0521011078

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**Proceedings of the Tennessee Topology Conference: Tennessee State University, June 10and 11, 1996**. And the book discusses many important topics in geometric group theory and topology, including Hopf's theory of ends; contractible manifolds and homology spheres; the Poincaré Conjecture; and Gromov's theory of CAT(0) spaces and groups. Finally, the book examines connections between Coxeter groups and some of topology's most famous open problems concerning aspherical manifolds, such as the Euler Characteristic Conjecture and the Borel and Singer conjectures. "This book is one of those that grows with the reader: A graduate student can learn many properties, details and examples of Coxeter groups, while an expert can read about aspects of recent results in the theory of Coxeter groups and use the book as a guide to the literature

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**Fundamentals of Three-dimensional Descriptive Geometry: Workbk**. Surgery refers to cutting out parts of the manifold and replacing it with a part of another manifold, matching up along the cut or boundary. This is closely related to, but not identical with, handlebody decompositions. It is a major tool in the study and classification of manifolds of dimension greater than 3. More technically, the idea is to start with a well-understood manifold M and perform surgery on it to produce a manifold M ′ having some desired property, in such a way that the effects on the homology, homotopy groups, or other interesting invariants of the manifold are known General Topology III: Paracompactness, Metrization, Coverings (Encyclopaedia of Mathematical Sciences Series). Generally, topology is employed to do the following: Manage coincident geometry (constrain how features share geometry). For example, adjacent polygons, such as parcels, have shared edges; street centerlines and the boundaries of census blocks have coincident geometry; adjacent soil polygons share edges; etc. Define and enforce data integrity rules (such as no gaps should exist between parcel features, parcels should not overlap, road centerlines should connect at their endpoints)

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**The Compactness operator in set theory and topology : MATHEMATICAL CENTRE TRACTS 21**. Thm.~\ref{thm:invariance} is of central importance. It states that \emph{the Euler-characteristic of a surface is a topological invariant}. Two surfaces that have the same Euler-characteristic share the same \emph{intrinsic} topology. However, we note that the Euler-characteristic does not define the homotopy type of a surface, since the embedding space is being ignored

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