Torus Actions and their Applications in Topology and Combinatorics

By V. Buchstaber, T. Panov. 2002

580 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/eece66d8e614159887c080136a543254b10ac7ff

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. M. Masuda
2. T. Panov
3. Frédéric Bosio
4. L. Meersseman
5. D. Suh
6. S. Gitler
7. S. Theriault
8. J. Grbić

In Discrete Mathematics and Combinatorics

1. T. Panov
2. M. Masuda
3. S. Theriault
4. J. Grbić
5. S. Gitler
6. Suyoung Choi
7. V. Buchstaber
8. D. Suh

In Geometry and Topology

1. T. Panov
2. M. Masuda
3. Marco A. M. Guaraco
4. F. C. Marques
5. A. Neves
6. S. Theriault
7. J. Grbić
8. S. Gitler

Citations in the corpus

• Toric topology (2012, methodology): “The space ZK is called a moment-angle complex and Buchstaber-Panov[9] used topological technique to study the cohomology ring of ZK and hence U(K).”
• Morse index of multiplicity one min-max minimal hypersurfaces (2015, background): “Every such cubical complex is homeomorphic to a finite simplicial complex and vice-versa (see Chapter 4 of [6]).”
• On Davis-Januszkiewicz homotopy types I; Formality and rationalisation (2003, background): “1), which plays a central rôle in [4].”
• The homotopy types of moment-angle complexes for flag complexes (2012, background): “Buchstaber and the second author [7] introduced homotopy theoretical models of both the moment-angle complex ZK and the Davis–Januszkiewicz space DJ(K) as a homotopy colimit construction of the product functor on the topological pairs (D(2), S(1)) and (CP, ∗) respectively, with the colimit taken ove”
• Rigidity problems in toric topology: A survey (2011, background): “Around 1990 Davis-Januszkiewicz [18] introduced what is now called a quasitoric manifold (see [1]), which is a topological analogue of a toric manifold.”
• Toric Topology (2012, unknown): “Set the bidegree (bdg) of the generators by bdg[1] = (0,0), bdg[T ] = (−1,2), bdg[D] = (0,2); ∂[1] = 0, ∂[T ] = 0, ∂[D] = [T ].”
• On the cohomology and their torsion of real toric objects (2013, background): “0 = {0,1} is its boundary. It should be noted that RZK is a manifold if K is a simplicial sphere, and there is a canonical Zm 2 -action on RZK which comes from the symmetry of (D1)m. See Chapter 6 of [3] for details. Definition 2.1 ([11]). A closed smooth manifold M of dimension n with an effective sm”
• Intersections of Quadrics, Moment-angle Manifolds and Connected Sums (2009, methodology): “P / are isomorphic as ungraded rings (see Bahri, Bendersky, Cohen and the first author [3]); this should also be a consequence of the other known descriptions of the cohomology rings [8; 10].”
• Classification problems of toric manifolds via topology (2007, methodology): “We refer the reader to a book [4] by Buchstaber-Panov for further development.”
• The homotopy type of the complement coordinate subspace arrangement (2006, background): “zkiewicz space is given as the cellular subcomplex DJ(K) = [ σ∈K BTσ ⊂ BTn. Buchstaber and Panov justified the name of this topological model by proving the following. Proposition 2.2 (Buchstaber-Panov[BP]). The cohomology of DJ(K) is isomorphic to the StanleyReisner ring Z[K]. Moreover, the inclusio”