منابع مشابه
Varieties in Finite Transformation Groups
The equivariant cohomology ring of a G-space X defines a homogeneous affine variety. Quillen [Q] and W. Y. Hsiang [Hs] have determined the relation between such varieties and the family of isotropy subgroups as well as their fixed point sets when dim X < oo. In modular representation theory, J. Carlson [Cj] introduced cohomological support varieties and rank varieties (the latter depending on t...
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We discuss boundedness and distortion in transformation groups. We show that the groups Diff0(R) and Diff (Rn) have the strong distortion property, whenever 0 ≤ r ≤ ∞, r 6= n+ 1. This implies in particular that every abstract length function on these groups is bounded. With related techniques we show that, for M a closed manifold or homeomorphic to the interior of a compact manifold with bounda...
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1. Introduction This note will summarize some of the recent work on topological groups and discuss a few topics in transformation groups mainly in S 3 and S 4. In one aspect of this subject, namely the relation of general locally compact groups to Lie groups, information is now fairly complete. However in most other aspects the situation is far less satisfactory and in many areas known results ...
متن کاملMethods of Transformation Groups
1. Continuous Transformation Groups 1.1. Local Transformation Groups 1.2. Lie Equations 1.3. Invariants 1.4. Invariant Manifolds 2. Invariant Differential Equations 2.1. The Continuation of Point Transformations 2.2. Defining Equation 2.3. Invariant and Partly Invariant Solutions 3. Tangential Transformations 3.1. Contact Transformations 3.2. Tangential Transformations of Finite and Infinite Or...
متن کاملIntroduction to Transformation Groups
These are the notes from a course that was an introduction to the theory of finite (or compact) transformation groups, including basic definitions and facts, standard examples, algebraic restrictions, fundamental constructions, all with an emphasis on group actions on manifolds in lowdimensional geometric topology. There is a focus on problems and results that have interesting versions in low d...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1970
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1970-0256372-x