Spectral Sequences on Combinatorial Simplicial Complexes

Authors:
Dmitry N. Kozlov
Affiliations:
School of Mathematics, Institute for Advanced Study, Olden Lane, Princeton, NJ, USA. kozlov@math.ias.edu
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
2001

Citing 4
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Abstract

The goal of this paper is twofold. First, we give an elementary introduction to the usage of spectral sequences in the combinatorial setting. Second we list a number of applications.In the first group of applications the simplicial complex is the nerve of a poset; we consider general posets and lattices, as well as partition-type posets. Our last application is of a different nature: the {\cal S}_n-quotient of the complex of directed forests is a simplicial complex whose cell structure is defined combinatorially.