Torus actions, combinatorial topology, and homological algebra (Q2780487)
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scientific article; zbMATH DE number 1729027
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Torus actions, combinatorial topology, and homological algebra |
scientific article; zbMATH DE number 1729027 |
Statements
Torus actions, combinatorial topology, and homological algebra (English)
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4 June 2002
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polyhedral manifolds
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toric varieties
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quasitoric manifolds
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bigraded Poincaré duality
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Stanley-Reisner space
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The paper is a survey of new results and open problems connected with fundamental combinatorial concepts, including polytopes, simplicial complexes, cubical complexes and arrangements of subspaces. Many important constructions are described that enable to study combinatorial objects by using commutative and homological algebra. The results of the paper establish solutions of some well-known topological problems.NEWLINENEWLINENEWLINEThe authors' remarkable techniques which they have carefully developed is a strong unifying theme of the paper. The amount of material covered in the paper is very large. The authors' presentation is attractive and lucid, quite suitable for a valuable reference for further research of the topic.
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