conley

 

Introduction to conley

The algebraic theory of connection and C-connection matrices is concerned with condensing the information of a graded module octahedron in a matrix called a connection matrix or C-connection matrix (cf. Mis95, Fra89). The package conley is more or less a tiny application of the more elaborate homological algebra package homalg. We are very much indebted to Stanislaus Maier-Paape, who initiated the joint Conley index seminar in Aachen, introduced us to the subject and explained us the fascinating dynamical side of the theory.

The main facilities of conley are the following:

• compute connection matrices
• compute C-connection matrices for a given initial complex C
• compute transition matrices
• allow restrictions dictated by symmetries (of the dynamical system)

Convention

Note that we apply morphisms from the right and hence we use the row convention for matrices. As one consequence we talk about lower triangular instead of upper triangular matrices.