
By Eldar Straume
During this ebook, the writer incorporates out a scientific research and development of all attainable differentiable (homotopy) G-spheres with 2-dimensional orbit house, the place G is any compact hooked up Lie crew. according to the geometric weight method category of half I, the potential orbit buildings are made up our minds, and the unique G-spheres are built by means of equivariant twisting of the orthogonal versions.
Read Online or Download Compact Connected Lie Transformation Groups on Spheres With Low Cohomogeneity - II PDF
Best algebraic geometry books
Mathematical Aspects of Geometric Modeling
This monograph examines intimately definite ideas which are valuable for the modeling of curves and surfaces and emphasizes the mathematical idea that underlies those principles. the 2 critical subject matters of the textual content are using piecewise polynomial illustration (this topic looks in a single shape or one other in each chapter), and iterative refinement, often known as subdivision.
Fractured Fractals and Broken Dreams: Self-Similar Geometry through Metric and Measure
Fractal styles have emerged in lots of contexts, yet what precisely is a development? How can one make detailed the buildings mendacity inside items and the relationships among them? This publication proposes new notions of coherent geometric constitution to supply a clean method of this conventional box. It develops a brand new idea of self-similarity referred to as "BPI" or "big items of itself," which makes the sector a lot more straightforward for individuals to go into.
From the experiences of the 1st printing of this ebook, released as quantity 6 of the Encyclopaedia of Mathematical Sciences: ". .. My normal impact is of a very great e-book, with a well-balanced bibliography, advised! "Medelingen van Het Wiskundig Genootschap, 1995". .. The authors supply the following an up to the moment consultant to the subject and its major purposes, together with a few new effects.
- Homotopy Theory Via Algebraic Geometry and Group Representations: Proceedings of a Conference on Homotopy Theory, March 23-27, 1997, Northwestern University (Contemporary Mathematics)
- Algebraic Integrability, Painlevé Geometry and Lie Algebras (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics)
- Geometric Methods in the Algebraic Theory of Quadratic Forms: Summer School, Lens, 2000 (Lecture Notes in Mathematics) (English and French Edition)
- Intersection theory, Edition: version 12 Jan 2006?
Additional resources for Compact Connected Lie Transformation Groups on Spheres With Low Cohomogeneity - II
Example text
The smoothness of the homeomorphisms involved will depend crucially on the next lemma. Let (H c L) be a spherical pair. It is well known that there is a unique representation *F : L —> 0(m+l) of cohomogeneity cQ¥) = 1, and with H as a principal isotropy group. Via this action of L we shall identify L/H with the unit sphere S m . 1 Let S m = L/H be as above and let G = L in (5). Then the corresponding homomorphism p in (5) maps each automorphism to an isometry, namely p : Aut(H; L) -> 0(m+l) c Diff(S m).
By [S4, p. 12], hence the last case is actually impossible. LOW COHOMOGENEITY ACTIONS 29 Inn(-; K) c Aut(-; K) denotes the subgroup of inner automorphisms, and Out(-; K) is the quotient group. 10 p maps Inn(H, L Q , L j ; K) into 0(q+l) if and only if R maps N K ( H , L 0 , L]) into 0(q+l). More precisely, let p n be the image of n by the composition N K ( H, L 0 , L i ) -> Inn(H, L 0 , L j ; K) P -> Diff^S^), where the first map is the natural surjective homomorphism. Then p n =
2), (6). , and assume also Aut(H, L 0 , L j ; K) e Aut(K'; K). 8 K is p -determined by its connected component K°. Proof By the above observation we shall assume K and K° are not C-equivalent. Then K/K° acts by reflection on the arc I' = S^/K0 and one of the two halves may be identified with I. 7 applies to this pair. Moreover, K' is a group of index 2 in K, say K = < K', y > where y 2 e K'. It remains to show that K is p -determined by K'. In terms of cross sections and associated triples we can make the following choices, namely H = H', L 0 = L' 0 , L j = < H, y > , L'j = yLQy" .