3,924 research outputs found
Computing âSmallâ 1âHomological Models for Commutative Differential Graded Algebras
We use homological perturbation machinery specific for the algebra category
[13] to give an algorithm for computing the differential structure of a small 1â
homological model for commutative differential graded algebras (briefly, CDGAs).
The complexity of the procedure is studied and a computer package in Mathematica
is described for determining such models.Ministerio de EducaciĂłn y Ciencia PB98â1621âC02â02Junta de AndalucĂa FQMâ014
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
The S-Matrix of superstring field theory
We show that the classical S-matrix calculated from the recently proposed
superstring field theories give the correct perturbative S-matrix. In the proof
we exploit the fact that the vertices are obtained by a field redefinition in
the large Hilbert space. The result extends to include the NS-NS subsector of
type II superstring field theory and the recently found equations of motions
for the Ramond fields. In addition, our proof implies that the S-matrix
obtained from Berkovits' WZW-like string field theory then agrees with the
perturbative S-matrix to all orders.Comment: 19 pages, 2 figure
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