By Michèle Audin
The cloth and references during this prolonged moment version of "The Topology of Torus activities on Symplectic Manifolds", released as quantity ninety three during this sequence in 1991, were up to date. Symplectic manifolds and torus activities are investigated, with a variety of examples of torus activities, for example on a few moduli areas. even supposing the ebook remains to be established on convexity effects, it comprises even more fabric, particularly plenty of new examples and routines.
Read or Download The Topology of Torus Actions on Symplectic Manifolds PDF
Similar differential geometry books
The notes from a suite of lectures writer added at nationwide Tsing-Hua collage in Hsinchu, Taiwan, within the spring of 1992. This notes is the a part of booklet "Thing Hua Lectures on Geometry and Analisys".
This ebook is concentrated at the interrelations among the curvature and the geometry of Riemannian manifolds. It comprises examine and survey articles in keeping with the most talks introduced on the overseas Congress
During this booklet, we learn theoretical and useful points of computing tools for mathematical modelling of nonlinear structures. a few computing recommendations are thought of, equivalent to tools of operator approximation with any given accuracy; operator interpolation concepts together with a non-Lagrange interpolation; tools of method illustration topic to constraints linked to options of causality, reminiscence and stationarity; tools of procedure illustration with an accuracy that's the top inside a given category of types; tools of covariance matrix estimation;methods for low-rank matrix approximations; hybrid tools in accordance with a mix of iterative tactics and top operator approximation; andmethods for info compression and filtering lower than clear out version should still fulfill regulations linked to causality and forms of reminiscence.
- Tight and Taut Submanifolds
- Gesammelte mathematische Werke
- Foliations on Riemannian Manifolds
- Integral Geometry, Radon Transforms and Complex Analysis: Lectures given at the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) ... 3-12, 1996
- Harmonic maps
- The topology of fibre bundles
Extra resources for The Topology of Torus Actions on Symplectic Manifolds
The interested readers may consult  for a rather complete list of definitions and references. 4. Appendix: Lie groups, Lie algebras, homogeneous spaces Recall that a group G is said to be a Lie group if this is both a group and a manifold, the two structures being compatible in the sense that the group operations are differentiable mappings. This structure is particularly interesting, because it allows one to use the infinitesimal calculus. The main examples are the ones used in this book, the (compact) torus Tn = Rn;zn, the (complex) torus (C*)n, the linear groups GL(n; R), GL(n; C) and their subgroups, O(n), U(n), and so on.
Calibrated almost complex structures Recall that en is a model for the symplectic vector spaces of dimension 2n. This is not accidental: on any symplectic manifold, there are almost complex structures. 2. CALIBRATED ALMOST COMPLEX STRUCTURES 53 A (linear) complex structure on a real vector space E is an endomorphism J of E such that J2 = -1. Analogously, an almost complex structure on a manifold W is a section J of the bundle End TW such that f; = - IdTxW for all x in W. For instance, if W is a complex manifold (namely a manifold with complex holomorphic change of local coordinates), its tangent space Tx W at any point has a natural structure of complex vector space and the multiplication by i is an almost complex structure.
Notice that it follows from the proposition that there is a whole neighborhood of 1 in the image of the exponential mapping. From this the next proposition is deduced. 5. In a connected Lie group, any element can be written as a product of exponentials. 4. APPENDIX: LIE GROUPS, LIE ALGEBRAS, HOMOGENEOUS SPACES 35 Proof A connected Lie group is path-connected. Let g be any element of the group G and let "( : [0, 1] ---+ G be a path from 1 to g. Let U be an open neighborhood of 1 that is included in the image of the exponential mapping.