89 research outputs found
Constructive Algebraic Topology
The classical ``computation'' methods in Algebraic Topology most often work
by means of highly infinite objects and in fact +are_not+ constructive. Typical
examples are shown to describe the nature of the problem. The Rubio-Sergeraert
solution for Constructive Algebraic Topology is recalled. This is not only a
theoretical solution: the concrete computer program +Kenzo+ has been written
down which precisely follows this method. This program has been used in various
cases, opening new research subjects and producing in several cases significant
results unreachable by hand. In particular the Kenzo program can compute the
first homotopy groups of a simply connected +arbitrary+ simplicial set.Comment: 24 pages, background paper for a plenary talk at the EACA Congress of
Tenerife, September 199
Computing spectral sequences
In this paper, a set of programs enhancing the Kenzo system is presented.
Kenzo is a Common Lisp program designed for computing in Algebraic Topology, in
particular it allows the user to calculate homology and homotopy groups of
complicated spaces. The new programs presented here entirely compute Serre and
Eilenberg-Moore spectral sequences, in particular the groups and differential
maps for arbitrary r. They also determine when the spectral sequence has
converged and describe the filtration of the target homology groups induced by
the spectral sequence
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