Cellular cochain algebras and torus actions

By I. Baskakov, V. Buchstaber, T. Panov. 2004

53 citations recorded by the source corpus.

. Cellular cochains do notadmit a functorial associative multiplication because a proper cellular diag-onal approximation does not exist in general. The construction of moment-angle complexes is a functor from the category of simplicial complexes to thecategory of spaces with torus action. We show that in this special case theproposed cellular approximation of the diagonal is associative and functorialwith respect to those maps of moment-angle complexes which are inducedby simplicial maps.The face ring of a complex K on the vertex set [m] = {1,...,m} isthe graded quotient ring Z[K] = Z[v

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f7c5e508235c3f360ccb23498b3bd845ebc88820

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In Discrete Mathematics and Combinatorics

1. T. Panov
2. Nigel Ray
3. M. Franz
4. V. Buchstaber
5. M. Masuda
6. L. Cai
7. Michael Joswig
8. S. Gitler

In Geometry and Topology

1. T. Panov
2. M. Franz
3. V. Buchstaber
4. Nigel Ray
5. M. Masuda
6. L. Cai
7. S. Theriault
8. J. Grbić

In Mathematical Physics

1. M. Franz
2. T. Panov
3. V. Buchstaber
4. Nigel Ray
5. L. Cai
6. M. Masuda

Citations in the corpus

• Categorical aspects of toric topology (2007, methodology): “The corresponding model for the inclusion Dσ → (S∞)σ × T V \σ is the projection ∧(U)⊗ S(σ)→ ∧(U)⊗ S(σ) / (ujvj = v(2) j = 0 for j ∈ σ), which reflects the fact that (ujvj = v2 j = 0 for j ∈ σ) is an acyclic ideal [3].”
• Surveys in Contemporary Mathematics: Cohomology of face rings, and torus actions (2005, background): “The proofs have been sketched in [5]; here”
• Toric Topology (2012, background): “The proof given here is taken from [21] and [49]; it establishes the isomorphism over the integers and works with the cellular cochains.”
• On products in a real moment-angle manifold (2014, background): “from Lemma2.7. When j i is even, i= 1;2;:::;m, this can be deduced from [BBCG10b, Proposition 6.2]. In particular, when J = (2) is constant with integers 2, R K (2) is the well-known algebra given in [BBP04] and [Pan08] for the cohomology of the moment-angle complex (D2;S1)K. In order to prove Theor”
• The integral cohomology of toric manifolds (2006, methodology): “In the language of toric varieties, these versions essentially correspond to arbitrary smooth toric varieties and rational coefficients (Buchstaber–Panov [5]) and to open toric subvarieties of Cr and integral coefficients (Baskakov–Buchstaber–Panov [1]).”