Torus graphs and simplicial posets

By H. Maeda, M. Masuda, T. Panov. 2005

64 citations recorded by the source corpus.

For several important classes of manifolds acted on by the torus, the information about the action can be encoded combinatorially by a regular n-valent graph with vector labels on its edges, which we refer to as the torus graph. By analogy with the GKM-graphs, we introduce the notion of equivariant cohomology of a torus graph, and show that it is isomorphic to the face ring of the associated simplicial poset. This extends a series of previous results on the equivariant cohomology of torus manifolds. As a primary combinatorial application, we show that a simplicial poset is Cohen?Macaulay if its face ring is Cohen?Macaulay. This completes the algebraic characterisation of Cohen?Macaulay posets initiated by Stanley. We also study blow-ups of torus graphs and manifolds from both the algebraic and the topological points of view.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/d9e743939b80c8c4c9ff5622a2e9b4d45f047d4e

How researchers see this paper

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In Algebra and Number Theory

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

In Computational Theory and Mathematics

  1. V. Buchstaber
  2. T. Panov
  3. M. Masuda

In Discrete Mathematics and Combinatorics

  1. T. Panov
  2. V. Buchstaber
  3. M. Masuda
  4. Nigel Ray
  5. D. Suh
  6. S. Gitler
  7. Frédéric Bosio
  8. L. Meersseman

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