**Contemporary Mathematics**

Volume: 460;
2008;
401 pp;
Softcover

MSC: Primary 14; 53; 55; 57;

Print ISBN: 978-0-8218-4486-1

Product Code: CONM/460

List Price: $112.00

Individual Member Price: $89.60

**Electronic ISBN: 978-0-8218-8139-2
Product Code: CONM/460.E**

List Price: $112.00

Individual Member Price: $89.60

# Toric Topology

Share this page *Edited by *
*Megumi Harada; Yael Karshon; Mikiya Masuda; Taras Panov*

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.

#### Table of Contents

# Table of Contents

## Toric Topology

- Contents v6 free
- Preface vii8 free
- List of Participants xiii14 free
- An invitation to toric topology: Vertex four of a remarkable tetrahedron 120 free
- Cohomological aspects of torus actions 2948
- A counterexample to a conjecture of Bosio and Meersseman 3756
- Symplectic quasi-states and semi-simplicity of quantum homology 4766
- Miraculous cancellation and Pick's theorem 7190
- Freeness of equivariant cohomology and mutants of compactified representations 87106
- Weighted hyperprojective spaces and homotopy invariance in orbifold cohomology 99118
- Homotopy theory and the complement of a coordinate subspace arrangement 111130
- 1. Introduction 112131
- 2. Homotopy theory 112131
- 3. Homotopy decompositions 114133
- 4. Toric Topology - main definitions and constructions 118137
- 5. The homotopy type of the complement of an arrangement 121140
- 6. Examples 122141
- 7. Topological extensions 126145
- 8. Applications 128147
- References 130149

- The quantization of a toric manifold is given by the integer lattice points in the moment polytope 131150
- Invariance property of orbifold elliptic genus for multi-fans 141160
- Act globally, compute locally: group actions, fixed points, and localization 179198
- Tropical toric geometry 197216
- The symplectic volume and intersection pairings of the moduli spaces of spatial polygons 209228
- Logarithmic functional and reciprocity laws 221240
- Orbifold cohomology reloaded 231250
- The geometry of toric hyperkähler varieties 241260
- Graphs of 2-torus actions 261280
- Classification problems of toric manifolds via topology 273292
- The quasi KO-types of certain toric manifolds 287306
- Categorical aspects of toric topology 293312
- A survey of hypertoric geometry and topology 323342
- On asymptotic partition functions for root systems 339358
- Torus actions of complexity one 349368
- Permutation actions on equivariant cohomology of flag varieties 365384
- K-theory of torus manifolds 385404
- On liftings of local torus actions to fiber bundles 391410

#### Readership

Graduate students and research mathematicians interested in different aspects of torus actions, such as topological, combinatorial, and symplectic or algebra-geometric.