In this note, we present some algebraic examples of multicomplexes whose differentials differ from those in the spectral sequences associated to the multicomplexes. The motivation for constructing examples showing the algebraic distinction between a multicomplex and its associated spectral sequence comes from the author's work on MorseBott homology with A. Banyaga [A. Banyaga and D. E. Hurtubise, MorseBott homology, Trans. Amer. Math. Soc. (to appear), arXiv:math/0612316v2].
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Applied Mathematics