Toric topology : international conference, May 29-June 3, 2006, Osaka City University, Osaka, Japan / Megumi Harada [and three others], editors.

Format:

Book

Conference/Event

Author/Creator:

International Conference on Toric Topology, Corporate Author.

Contributor:

Harada, Megumi, editor.

Conference Name:

International Conference on Toric Topology (2006 : Osaka City University)

International Conference on Toric Topology

Series:

Contemporary mathematics (American Mathematical Society). 0271-4132 460

Contemporary mathematics, 0271-4132 ; 460 0271-4132

Language:

English

Subjects (All):

Torus (Geometry)--Congresses.

Torus (Geometry).

Toric varieties--Congresses.

Toric varieties.

Topology--Congresses.

Topology.

Physical Description:

1 online resource (xvii, 401 p. )

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2008]

Language Note:

English

Summary:

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.

Contents:

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 decompositions

4. 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 cohomology

4. Combinatorial localization and polytope decompositions

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 hyperkähler 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 systems.

Torus 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.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references.

Description based on print version record.

Other Format:

Print version: International Conference on Toric Topology (2006 : Osaka City University) Toric topology : international conference, May 29-June 3, 2006, Osaka City University, Osaka, Japan.

ISBN:

0-8218-8139-6

0-8218-4486-5