next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
SpectralSequences :: SpectralSequencePageMap

SpectralSequencePageMap -- the type of all spectral sequence page maps

Description

A (homological, or lower index) spectral sequence page map consists of:

1. A fixed integer r ≥0 , the page number;

2. A collection of homomorphisms {drp,q: Erp,q →Erp-r,q+r-1} for p,q ∈ℤ, r ≥0 such that drp,q drp+r,q-r+1 = 0.

Alternatively a (cohomological, or upper index) spectral sequence page consists of:

1’. A fixed integer r ≥0, the page number;

2’. A collection of homomorphisms {drp,q: Erp,q →Erp+r,q-r+1} for p,q ∈ℤ, r ≥0 such that drp,q drp-r,q+r-1 = 0.

The type SpectralSequencePageMap is a data type for working with spectral sequences and the differentials on the pages of a spectral sequence.

See also

Functions and methods returning a spectral sequence page map :

Methods that use a spectral sequence page map :

For the programmer

The object SpectralSequencePageMap is a type, with ancestor classes PageMap < MutableHashTable < HashTable < Thing.