5 research outputs found
Universal complexes in toric topology
We study combinatorial and topological properties of the universal complexes
and whose simplices are certain
unimodular subsets of . We calculate their -vectors
and their Tor-algebras, show that they are shellable but not shifted, and find
their applications in toric topology and number theory. We showed that the
Lusternick-Schnirelmann category of the moment angle complex of
is , provided is an odd prime, and the
Lusternick-Schnirelmann category of the moment angle complex of
is . Based on the universal complexes, we
introduce the Buchstaber invariant for a prime number
Facet colouring of nestohedra
A proper colouring of a polytope is a surjective function from the set of facetsto a set ofmcolours such that every two facets associated with the same colour areseparated, i.e. have no vertex in common. The chromatic number of a polytope is theminimalmsuch that there exists a proper colouring of its facets inmcolours. Thistalk presents the chromatic numbers of associahedra and some others interestingmembers of the family of nestohedra
The Law of Large Numbers for the bigraded Betti numbers of the random moment-angle complex
2 pages, no figures. The translation of the article to Russian is kindly provided by Ivan Limonchenko, but is at the moment not included in the submissionThis note announces recent exciting progress on the frontier between algebraic topology and probability theory. It is intended for a journal which publishes such announcements (without an abstract, typically in Russian). A description of a larger work in progress is included in the concluding remarks
Toric objects associated with the dodecahedron
In this paper we illustrate a tight interplay between homotopy theory and combinatorics within toric topology by explicitly calculating homotopy and combinatorial invariants of toric objects associated with the dodecahedron. In particular, we calculate the cohomology ring of the (complex and real) moment-angle manifolds over the dodecahedron, and of a certain quasitoric manifold and of a related small cover. We finish by studying Massey products in the cohomology ring of moment-angle manifolds over the dodecahedron and how the existence of nontrivial Massey products influences the behaviour of the Poincaré series of the corresponding Pontryagin algebra.</p