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 manifold interact in a rich variety of ways, thus illuminating subtle aspects of both the combinatorics and the equivariant topology. Many of the motivations and guiding principles of the field are provided by (though not limited to) the theory of toric varieties in algebraic geometry as well as that of symplectic toric manifolds in symplectic geometry. This volume is the proceedings of the International Conference on Toric Topology held in Osaka in May-June 2006. It contains about 25 research and survey articles written by conference speakers, covering many different aspects of, and approaches to, torus actions, such as those mentioned above.Some of the manuscripts are survey articles, intended to give a broad overview of an aspect of the subject; all manuscripts consciously aim to be accessible to a broad reading audience of students and researchers interested in the interaction of the subjects involved. We hope that this volume serves as an enticing invitation to this emerging field.
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978-0-8218-4486-1 (9780821844861)
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Schweitzer Klassifikation
An invitation to toric topology: Vertex four of a remarkable tetrahedron by V. M. Buchstaber and N. Ray Cohomological aspects of torus actions by C. Allday A counterexample to a conjecture of Bosio and Meersseman by D. Allen and J. La Luz Symplectic quasi-states and semi-simplicity of quantum homology by M. Entov and L. Polterovich Miraculous cancellation and Pick's theorem by K. Feldman Freeness of equivariant cohomology and mutants of compactified representations by M. Franz and V. Puppe Weighted hyperprojective spaces and homotopy invariance in orbifold cohomology by R. Goldin Homotopy theory and the complement of a coordinate subspace arrangement by J. Grbic The quantization of a toric manifold is given by the integer lattice points in the moment polytope by M. D. Hamilton Invariance property of orbifold elliptic genus for multi-fans by A. Hattori Act globally, compute locally: Group actions, fixed points, and localization by T. S. Holm Tropical toric geometry by T. Kajiwara The symplectic volume and intersection pairings of the moduli spaces of spatial polygons by Y. Kamiyama Logarithmic functional and reciprocity laws by A. Khovanskii Orbifold cohomology reloaded by T. Kimura The geometry of toric hyperkahler varieties by H. Konno Graphs of 2-torus actions by Z. Lu Classification problems of toric manifolds via topology by M. Masuda and D. Y. Suh The quasi $KO$-types of certain toric manifolds by Y. Nishimura Categorical aspects of toric topology by T. E. Panov and N. Ray A survey of hypertoric geometry and topology by N. J. Proudfoot On asymptotic partition functions for root systems by T. Takakura Torus actions of complexity one by D. Timashev Permutation actions on equivariant cohomology of flag varieites by J. S. Tymoczko K-theory of torus manifolds by V. Uma On liftings of local torus actions to fiber bundles by T. Yoshida.
