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Toric Topology.
Toric topology is the study of algebraic, differential, symplectic-geometric, combinatorial, and homotopy-theoretic aspects of a particular class of torus actions whose quotients are highly structured. The combinatorial properties of this quotient and the equivariant topology of the original manifol...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
2008.
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| Colección: | Contemporary Mathematics Ser.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Intro; Contents; Preface; List of Participants; An invitation to toric topology: Vertex four of a remarkable tetrahedron; Cohomological aspects of torus actions; A counterexample to a conjecture of Bosio and Meersseman; Symplectic quasi-states and semi-simplicity of quantum homology; Miraculous cancellation and Pick's theorem; Freeness of equivariant cohomology and mutants of compactified representations; Weighted hyperprojective spaces and homotopy invariance in orbifold cohomology; Homotopy theory and the complement of a coordinate subspace arrangement; 1. Introduction; 2. Homotopy theory.
- 3. Homotopy decompositions4. Toric Topology
- main definitions and constructions; 5. The homotopy type of the complement of an arrangement; 6. Examples; 7. Topological extensions; 8. Applications; References; The quantization of a toric manifold is given by the integer lattice points in the moment polytope; Invariance property of orbifold elliptic genus for multi-fans; Act globally, compute locally: group actions, fixed points, and localization; Introduction; 1. A brief review of the symplectic category; 2. Equivariant cohomology and localization theorems.
- 3. Using localization to compute equivariant cohomology4. Combinatorial localization and polytope decompositions; References; Tropical toric geometry; The symplectic volume and intersection pairings of the moduli spaces of spatial polygons; Logarithmic functional and reciprocity laws; Orbifold cohomology reloaded; The geometry of toric hyperkÃÞhler varieties; Graphs of 2-torus actions; Classification problems of toric manifolds via topology; The quasi KO-types of certain toric manifolds; Categorical aspects of toric topology; A survey of hypertoric geometry and topology.
- On asymptotic partition functions for root systemsTorus actions of complexity one; Permutation actions on equivariant cohomology of flag varieties; K-theory of torus manifolds; On liftings of local torus actions to fiber bundles.