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 May 23, 2024

Page view(s)

348
checked on May 9, 2024

Google ScholarTM

Check

Altmetric

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.