eBook ISBN:  9780821881392 
Product Code:  CONM/460.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821881392 
Product Code:  CONM/460.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 460; 2008; 401 ppMSC: Primary 14; 53; 55; 57
Toric topology is the study of algebraic, differential, symplecticgeometric, combinatorial, and homotopytheoretic 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.
ReadershipGraduate students and research mathematicians interested in different aspects of torus actions, such as topological, combinatorial, and symplectic or algebrageometric.

Table of Contents

Articles

Victor M. Buchstaber and Nigel Ray — An invitation to toric topology: vertex four of a remarkable tetrahedron [ MR 2428345 ]

Christopher Allday — Cohomological aspects of torus actions [ MR 2428346 ]

David Allen and José La Luz — A counterexample to a conjecture of Bosio and Meersseman [ MR 2428347 ]

Michael Entov and Leonid Polterovich — Symplectic quasistates and semisimplicity of quantum homology [ MR 2428348 ]

K. E. Feldman — Miraculous cancellation and Pick’s theorem [ MR 2428349 ]

Matthias Franz and Volker Puppe — Freeness of equivariant cohomology and mutants of compactified representations [ MR 2428350 ]

Rebecca Goldin — Weighted hyperprojective spaces and homotopy invariance in orbifold cohomology [ MR 2428351 ]

Jelena Grbić — Homotopy theory and the complement of a coordinate subspace arrangement [ MR 2428352 ]

Mark D. Hamilton — The quantization of a toric manifold is given by the integer lattice points in the moment polytope [ MR 2428353 ]

Akio Hattori — Invariance property of orbifold elliptic genus for multifans [ MR 2428354 ]

Tara S. Holm — Act globally, compute locally: group actions, fixed points, and localization [ MR 2428355 ]

Takeshi Kajiwara — Tropical toric geometry [ MR 2428356 ]

Yasuhiko Kamiyama — The symplectic volume and intersection pairings of the moduli spaces of spatial polygons [ MR 2428357 ]

Askold Khovanskii — Logarithmic functional and reciprocity laws [ MR 2428358 ]

Takashi Kimura — Orbifold cohomology reloaded [ MR 2428359 ]

Hiroshi Konno — The geometry of toric hyperkähler varieties [ MR 2428360 ]

Zhi Lü — Graphs of 2torus actions [ MR 2428361 ]

Mikiya Masuda and Dong Youp Suh — Classification problems of toric manifolds via topology [ MR 2428362 ]

Yasuzo Nishimura — The quasi $KO$types of certain toric manifolds [ MR 2428363 ]

Taras E. Panov and Nigel Ray — Categorical aspects of toric topology [ MR 2428364 ]

Nicholas J. Proudfoot — A survey of hypertoric geometry and topology [ MR 2428365 ]

Tatsuru Takakura — On asymptotic partition functions for root systems [ MR 2428366 ]

Dmitri Timashev — Torus actions of complexity one [ MR 2428367 ]

Julianna S. Tymoczko — Permutation actions on equivariant cohomology of flag varieties [ MR 2428368 ]

V. Uma — $K$theory of torus manifolds [ MR 2428369 ]

Takahiko Yoshida — On liftings of local torus actions to fiber bundles [ MR 2428370 ]


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Toric topology is the study of algebraic, differential, symplecticgeometric, combinatorial, and homotopytheoretic 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.
Graduate students and research mathematicians interested in different aspects of torus actions, such as topological, combinatorial, and symplectic or algebrageometric.

Articles

Victor M. Buchstaber and Nigel Ray — An invitation to toric topology: vertex four of a remarkable tetrahedron [ MR 2428345 ]

Christopher Allday — Cohomological aspects of torus actions [ MR 2428346 ]

David Allen and José La Luz — A counterexample to a conjecture of Bosio and Meersseman [ MR 2428347 ]

Michael Entov and Leonid Polterovich — Symplectic quasistates and semisimplicity of quantum homology [ MR 2428348 ]

K. E. Feldman — Miraculous cancellation and Pick’s theorem [ MR 2428349 ]

Matthias Franz and Volker Puppe — Freeness of equivariant cohomology and mutants of compactified representations [ MR 2428350 ]

Rebecca Goldin — Weighted hyperprojective spaces and homotopy invariance in orbifold cohomology [ MR 2428351 ]

Jelena Grbić — Homotopy theory and the complement of a coordinate subspace arrangement [ MR 2428352 ]

Mark D. Hamilton — The quantization of a toric manifold is given by the integer lattice points in the moment polytope [ MR 2428353 ]

Akio Hattori — Invariance property of orbifold elliptic genus for multifans [ MR 2428354 ]

Tara S. Holm — Act globally, compute locally: group actions, fixed points, and localization [ MR 2428355 ]

Takeshi Kajiwara — Tropical toric geometry [ MR 2428356 ]

Yasuhiko Kamiyama — The symplectic volume and intersection pairings of the moduli spaces of spatial polygons [ MR 2428357 ]

Askold Khovanskii — Logarithmic functional and reciprocity laws [ MR 2428358 ]

Takashi Kimura — Orbifold cohomology reloaded [ MR 2428359 ]

Hiroshi Konno — The geometry of toric hyperkähler varieties [ MR 2428360 ]

Zhi Lü — Graphs of 2torus actions [ MR 2428361 ]

Mikiya Masuda and Dong Youp Suh — Classification problems of toric manifolds via topology [ MR 2428362 ]

Yasuzo Nishimura — The quasi $KO$types of certain toric manifolds [ MR 2428363 ]

Taras E. Panov and Nigel Ray — Categorical aspects of toric topology [ MR 2428364 ]

Nicholas J. Proudfoot — A survey of hypertoric geometry and topology [ MR 2428365 ]

Tatsuru Takakura — On asymptotic partition functions for root systems [ MR 2428366 ]

Dmitri Timashev — Torus actions of complexity one [ MR 2428367 ]

Julianna S. Tymoczko — Permutation actions on equivariant cohomology of flag varieties [ MR 2428368 ]

V. Uma — $K$theory of torus manifolds [ MR 2428369 ]

Takahiko Yoshida — On liftings of local torus actions to fiber bundles [ MR 2428370 ]