Authors: | Limonchenko, Ivan | Title: | Bigraded Betti numbers of certain simple polytopes | Journal: | Mathematical Notes | Volume: | 94 | First page: | 351 | Last page: | 363 | Issue Date: | 2013 | Rank: | M23 | ISSN: | 0001-4346 | DOI: | 10.1134/S000143461309006X | Abstract: | The bigraded Betti numbers β−i,2j (P ) of a simple polytope P are the dimensions of the bigraded components of the Tor groups of the face ring k[P ]. The numbers β−i,2j (P ) reflect the combinatorial structure of P , as well as the topological structure of the corresponding moment-angle manifold ZP ; thus, they find numerous applications in combinatorial commutative algebra and toric topology. We calculate certain bigraded Betti numbers of the type β−i,2(i+1) for associahedra and apply the calculation of bigraded Betti numbers for truncation polytopes to study the topology of their moment-angle manifolds. Presumably, for these two series of simple polytopes, the numbers β−i,2j (P ) attain their minimum and maximum values among all simple polytopes P of fixed dimension with a given number of facets. |
Keywords: | bigraded Betti numbers of a simple polytope | simple convex polytope | Stasheff polytope | associahedron | truncation polytope | stacked polytope | moment-angle manifold | Publisher: | Springer Link |
Show full item record
SCOPUSTM
Citations
1
checked on Sep 16, 2024
Page view(s)
5
checked on Sep 16, 2024
Google ScholarTM
Check
Altmetric
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.