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Home > Art, Film & Photography > Group Actions: Group Action, Orbifold, Geometric Invariant Theory, Principal Bundle, Quotient Space, Flow, Moment Map, Fundamental Domain
Group Actions: Group Action, Orbifold, Geometric Invariant Theory, Principal Bundle, Quotient Space, Flow, Moment Map, Fundamental Domain

Group Actions: Group Action, Orbifold, Geometric Invariant Theory, Principal Bundle, Quotient Space, Flow, Moment Map, Fundamental Domain


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About the Book

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 28. Chapters: Group action, Orbifold, Geometric invariant theory, Principal bundle, Quotient space, Flow, Moment map, Fundamental domain, Orbit, Crossed module, Character variety, Equivariant map, Properly discontinuous action, Group with operators, Equivariant cohomology, Hilbert-Smith conjecture, Free regular set, Continuous symmetry, Borel fixed-point theorem, CAT(k) group, Cocompact group action. Excerpt: This terminology should not be blamed on me. It was obtained by a democratic process in my course of 1976-77. An orbifold is something with many folds; unfortunately, the word "manifold" already has a different definition. I tried "foldamani," which was quickly displaced by the suggestion of "manifolded." After two months of patiently saying "no, not a manifold, a manifol," we held a vote, and "orbifold" won. In the mathematical disciplines of topology, geometry, and geometric group theory, an orbifold (for "orbit-manifold") is a generalization of a manifold. It is a topological space (called the underlying space) with an orbifold structure (see below). The underlying space locally looks like the quotient space of a Euclidean space under the linear action of a finite group. Definitions of orbifold have been given several times: by Satake in the context of automorphic forms in the 1950s under the name V-manifold; by Thurston in the context of the geometry of 3-manifolds in the 1970s when he coined the name orbifold, after a vote by his students; and by Haefliger in the 1980s in the context of Gromov's programme on CAT(k) spaces under the name orbihedron. The definition of Thurston will be described here: it is the most widely used and is applicable in all cases. Mathematically, orbifolds arose first as surfaces with singular points long before they were formally defined. One of the first classical examples arose in the theory...


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Product Details
  • ISBN-13: 9781157066439
  • Publisher: Books LLC, Wiki Series
  • Publisher Imprint: Books LLC, Wiki Series
  • Height: 246 mm
  • No of Pages: 108
  • Spine Width: 6 mm
  • Weight: 209 gr
  • ISBN-10: 1157066437
  • Publisher Date: 29 Aug 2011
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: Group Action, Orbifold, Geometric Invariant Theory, Principal Bundle, Quotient Space, Flow, Moment Map, Fundamental Domain
  • Width: 189 mm


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