Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- Computational Commutative Algebra and Combinatorics, T. Hibi, ed. (Tokyo: Mathematical Society of Japan, 2002), 53 - 64
Algebraic Shifting and Spectral Sequences
There is a canonical spectral sequence associated to any filtration of simplicial complexes. Algebraically shifting a finite filtration of simplicial complexes produces a new filtration of shifted complexes.
We prove that certain sums of the dimensions of the limit terms of the spectral sequence of a filtration weakly decrease by algebraically shifting the filtration. A key step is the combinatorial interpretation of the dimensions of the limit terms of the spectral sequence of a filtration consisting of near-cones.
Received: 29 May 2000
First available in Project Euclid: 31 December 2018
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 55T05: General
Secondary: 05A20: Combinatorial inequalities 05E99: None of the above, but in this section 52B05: Combinatorial properties (number of faces, shortest paths, etc.) [See also 05Cxx] 55N99: None of the above, but in this section
Duval, Art M. Algebraic Shifting and Spectral Sequences. Computational Commutative Algebra and Combinatorics, 53--64, Mathematical Society of Japan, Tokyo, Japan, 2002. doi:10.2969/aspm/03310053. https://projecteuclid.org/euclid.aspm/1546230152