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catalog contributor b12481573.
catalog contributor b12481574.
catalog created "c2002.".
catalog date "2002".
catalog date "c2002.".
catalog dateCopyrighted "c2002.".
catalog description "3.1. Stanley-Reisner face rings of simplicial complexes -- 3.2. Cohen-Macaulay rings and complexes -- 3.3. Homological algebra background -- 3.4. Homological properties of face rings: Tor-algebras and Betti numbers -- 3.5. Gorenstein complexes and Dehn-Sommerville equations -- Ch. 4. Cubical complexes -- 4.1. Definitions and cubical maps -- 4.2. Cubical subdivisions and simple polytopes and simplicial complexes -- Ch. 5. Toric and quasitoric manifolds -- 5.1. Toric varieties -- 5.2. Quasitoric manifolds -- 5.3. Stably complex structures, and quasitoric representatives in cobordism classes.".
catalog description "5.4. Combinatorial formulae for Hirzebruch genera of quasitoric manifolds -- 5.5. Classification problems -- Ch. 6. Moment-angle complexes -- 6.1. Moment-angle manifolds Z[subscript P] defined by simple polytopes -- 6.2. General moment-angle complexes Z[subscript K] -- 6.3. Cell decompositions of moment-angle complexes -- 6.4. Moment-angle complexes corresponding to joins, connected sums and bistellar moves -- 6.5. Borel constructions and Davis-Januszkiewicz space -- 6.6. Walk around the construction of Z[subscript K]: generalizations, analogues and additional comments.".
catalog description "Ch. 1. Polytopes -- 1.1. Definitions and main constructions -- 1.2. Face vectors and Dehn Sommerville equations -- 1.3. The g-theorem -- 1.4. Upper Bound and Lower Bound theorems -- 1.5. Stanley-Reisner face rings of simple polytopes -- Ch. 2. Topology and combinatorics of simplicial complexes -- 2.1. Abstract simplicial complexes and polyhedrons -- 2.2. Basic PL topology, and operations with simplicial complexes -- 2.3. Simplicial spheres -- 2.4. Triangulated manifolds -- 2.5. Bistellar moves -- Ch. 3. Commutative and homological algebra of simplicial complexes.".
catalog description "Ch. 7. Cohomology of moment-angle complexes and combinatorics of triangulated manifolds -- 7.1. The Eilenberg-Moore spectral sequence -- 7.2. Cohomology algebra of Z[subscript K] -- 7.3. Bigraded Betti numbers of Z[subscript K]: the case of general K -- 7.4. Bigraded Betti numbers of Z[subscript K]: the case of spherical K -- 7.5. Partial quotients of Z[subscript P] -- 7.6. Bigraded Poincare duality and Dehn-Sommerville equations.".
catalog description "Ch. 8. Cohomology rings of subspace arrangement complements -- 8.1. General arrangements and their complements -- 8.2. Coordinate subspace arrangements and the cohomology of Z[subscript K] -- 8.3. Diagonal subspace arrangements and the cohomology of [Omega]Z[subscript K].".
catalog description "Includes bibliographical references (p. 135-140) and index.".
catalog extent "viii, 144 p. :".
catalog identifier "0821831860 (alk. paper)".
catalog isPartOf "University lecture series (Providence, R.I.) ; 24.".
catalog isPartOf "University lecture series, 1047-3998 ; v. 24".
catalog issued "2002".
catalog issued "c2002.".
catalog language "eng".
catalog publisher "Providence, R.I. : American Mathematical Society,".
catalog subject "514/.3 21".
catalog subject "Combinatorial analysis.".
catalog subject "QA613.2 .B83 2002".
catalog subject "Topological spaces.".
catalog subject "Torus (Geometry)".
catalog tableOfContents "3.1. Stanley-Reisner face rings of simplicial complexes -- 3.2. Cohen-Macaulay rings and complexes -- 3.3. Homological algebra background -- 3.4. Homological properties of face rings: Tor-algebras and Betti numbers -- 3.5. Gorenstein complexes and Dehn-Sommerville equations -- Ch. 4. Cubical complexes -- 4.1. Definitions and cubical maps -- 4.2. Cubical subdivisions and simple polytopes and simplicial complexes -- Ch. 5. Toric and quasitoric manifolds -- 5.1. Toric varieties -- 5.2. Quasitoric manifolds -- 5.3. Stably complex structures, and quasitoric representatives in cobordism classes.".
catalog tableOfContents "5.4. Combinatorial formulae for Hirzebruch genera of quasitoric manifolds -- 5.5. Classification problems -- Ch. 6. Moment-angle complexes -- 6.1. Moment-angle manifolds Z[subscript P] defined by simple polytopes -- 6.2. General moment-angle complexes Z[subscript K] -- 6.3. Cell decompositions of moment-angle complexes -- 6.4. Moment-angle complexes corresponding to joins, connected sums and bistellar moves -- 6.5. Borel constructions and Davis-Januszkiewicz space -- 6.6. Walk around the construction of Z[subscript K]: generalizations, analogues and additional comments.".
catalog tableOfContents "Ch. 1. Polytopes -- 1.1. Definitions and main constructions -- 1.2. Face vectors and Dehn Sommerville equations -- 1.3. The g-theorem -- 1.4. Upper Bound and Lower Bound theorems -- 1.5. Stanley-Reisner face rings of simple polytopes -- Ch. 2. Topology and combinatorics of simplicial complexes -- 2.1. Abstract simplicial complexes and polyhedrons -- 2.2. Basic PL topology, and operations with simplicial complexes -- 2.3. Simplicial spheres -- 2.4. Triangulated manifolds -- 2.5. Bistellar moves -- Ch. 3. Commutative and homological algebra of simplicial complexes.".
catalog tableOfContents "Ch. 7. Cohomology of moment-angle complexes and combinatorics of triangulated manifolds -- 7.1. The Eilenberg-Moore spectral sequence -- 7.2. Cohomology algebra of Z[subscript K] -- 7.3. Bigraded Betti numbers of Z[subscript K]: the case of general K -- 7.4. Bigraded Betti numbers of Z[subscript K]: the case of spherical K -- 7.5. Partial quotients of Z[subscript P] -- 7.6. Bigraded Poincare duality and Dehn-Sommerville equations.".
catalog tableOfContents "Ch. 8. Cohomology rings of subspace arrangement complements -- 8.1. General arrangements and their complements -- 8.2. Coordinate subspace arrangements and the cohomology of Z[subscript K] -- 8.3. Diagonal subspace arrangements and the cohomology of [Omega]Z[subscript K].".
catalog title "Torus actions and their applications in topology and combinatorics / Victor M. Buchstaber, Taras E. Panov.".
catalog type "text".