A spectral sequence for polyhedral products

作者：Bahri A; Bendersky M^*; Cohen F R; Gitler S

来源：Advances in Mathematics, 2017, 308: 767-814.

DOI：10.1016/j.aim.2016.12.028

• Polyhedral products
• Cohomology
• Spectral sequences
• Stable splittings
• Moment-angle complexes
• Simplicial complexes

The purpose of this paper is to exhibit fine structure for polyhedral products Z(K; ((X) under bar, (A) under bar)) and polyhedral smash products (Z) over cap (K; ((X) under bar, (A) under bar)) where moment -angle complexes are special cases in which (X, A) = (D-2, S-1). There are three main parts to this paper.
(1) One part gives a natural filtration of the polyhedral product together with properties of the resulting spectral sequence in Theorem 2.15. Applications of this spectral sequence are given.
(2) The second part gives a homological decomposition of (Z) over cap (K; ((X) under bar, (A) under bar)) in case ((X) under bar, (A) under bar) consists of CW pairs by using part 1.
(3) Applications to the ring structure of Z(K; ((X) under bar, (A) under bar)) are given for CW-pairs (X, A) satisfying suitable freeness conditions.

• 出版日期2017-2-21