Torus actions, combinatorial topology, and homological algebra
type: Item
instance of: scholarly article
title: Torus actions, combinatorial topology, and homological algebra
zbMATH Open document ID: 1010.52011
published in: Russian Mathematical Surveys
publication date: 2002-06-04T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0010073
Mathematics Subject Classification ID: 52B70
Mathematics Subject Classification ID: 57Q15
Mathematics Subject Classification ID: 14M25
Mathematics Subject Classification ID: 57R19
zbMATH DE Number: 1729027
zbMATH Keywords: polyhedral manifolds
zbMATH Keywords: toric varieties
zbMATH Keywords: quasitoric manifolds
zbMATH Keywords: bigraded Poincaré duality
zbMATH Keywords: Stanley-Reisner space
author: V. M. Buchstaber
author: T. E. Panov
MaRDI profile type: Publication
arXiv ID: math/0010073
OpenAlex ID: W2054608537
DOI: 10.1070/RM2000V055N05ABEH000320
review text: 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.
reviewed by: Akrur Behera
description: scientific article; zbMATH DE number 1729027