156 lines
4.5 KiB
TeX
156 lines
4.5 KiB
TeX
\documentclass[11pt]{report}
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\usepackage{makeidx}
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\usepackage{graphics}
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\usepackage{amssymb}
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\pagestyle{headings}
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\makeindex
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\parindent=0mm
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%\textwidth=6.0in
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%\textheight=8.0in
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%\oddsidemargin=-.35i
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%\evensidemargin=-.35in
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%\topmargin=-.50in
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\newtheorem{thr}{Theorem}
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%\font\bb=msym10
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\def\N{{\Bbb N}}
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\def\Z{{\Bbb Z}}
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\def\R{{\Bbb R}}
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%
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% macros pour les diagrammes rectangulaires
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%
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\def\hfl#1#2{\smash{\mathop{\hbox to 15mm{\rightarrowfill}}
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\limits^{\scriptstyle#1}_{\scriptstyle#2}}}
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%
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\def\hflr#1#2{\smash{\mathop{\hbox to 15mm{\rightarrowfill}}
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\limits^{\scriptstyle#1}_{\scriptstyle#2}}}
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\def\hfll#1#2{\smash{\mathop{\hbox to 15mm{\leftarrowfill}}
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\limits^{\scriptstyle#1}_{\scriptstyle#2}}}
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\def\vfl#1#2{\llap{$\scriptstyle #1$}\left\downarrow
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\vbox to 7mm{}\right.\rlap{$\scriptstyle #2$}}
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\def\vflu#1#2{\llap{$\scriptstyle #1$}\left\uparrow
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\vbox to 7mm{}\right.\rlap{$\scriptstyle #2$}}
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%
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\def\diagram#1{\def\normalbaselines{\baselineskip=0pt
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\lineskip=10pt\lineskiplimit=1pt} \matrix{#1}}
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%
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% macro tvi pour les lignes verticales et horizontales dans un tableau
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%
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\def\tvi{\vrule height 12pt depth 5pt width 0pt}
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\def\tv{\tvi\vrule}
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\begin{document}
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\pagenumbering{roman}
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\begin{titlepage}
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\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\
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\begin{center}
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{\huge KENZO} \\
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\ \\
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{\Large a Symbolic Software} \\
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for \\
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{\Large Effective Homology Computation}
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\vskip 0.5cm
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-----
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\vskip 0.5cm
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Julio Rubio Garcia\\
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Francis Sergeraert \\
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Yvon Siret
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\vskip 0.20cm
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-----
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\vskip 0.20cm
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Institut Fourier \\
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Grenoble, France \\
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\vskip 0.20cm
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-----
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\vskip 0.20cm
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\end{center}
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\vskip 0.5cm
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This document is a user guide for the
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basic modules of the Effective Ho\-mo\-lo\-gy Software (Kenzo Version 1998). \\
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It is also available by anonymous ftp ({\bf ftp fourier.ujf-grenoble.fr})
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in the directory {\bf /pub/KENZO}. \\
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\vskip 0.5cm
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\begin{center}
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{\em \today} \\
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\end{center}
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\end{titlepage}
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\vskip 1in
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\centerline {FOREWORD}
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\vskip 0.5in
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The {\bf Kenzo} program implements the general ideas of the second author
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about \emph{Effective Homology}\footnote{{\bf Francis Sergeraert.}
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\emph{The computability problem in algebraic topology}.
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Advances in Mathematics, 1994, vol. 104, pp 1-29.},
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mainly around the Serre and Eilenberg--Moore spectral sequences.
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The first author (re--) discovered the importance
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of the \emph{Basic Perturbation Lemma} in these questions, already
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noted by Victor Gugenheim\footnote{{\bf V.K.A.M. Gugenheim.}
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\emph{On a perturbation theory for the homology of the loop space}.
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Journal of Pure and Applied Algebra, 1982, vol. 25, pp 197-205.}
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and this program directly
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implements and directly uses this ``lemma'' which should be called the
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\emph{Fundamental Theorem of Algebraic Topology}. The first version of the program,
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called {\bf EAT}, was written in 1989-90 by the first and the second authors.
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It has been demonstrated in several universities: France: Grenoble and
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Montpellier, Belgium: Louvain-la-Neuve, Italy: Genoa and Pisa,
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Sweden: Stockolm, Japan:
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Sapporo, Morioka, Urawa, Tokyo, Kyoto, Nara, Osaka and Hiroshima.
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\par
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In this {\bf Kenzo} version, numerous improvements have been integrated in comparison with
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{\bf EAT}.
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\begin{enumerate}
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\item Standard CLOS (Common Lisp Object System) techniques.
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\item Use of the Zermelo theorem about ordered sets (!): any set can be
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well ordered and this remark gives important new ideas to improve
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execution speed.
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\item Better memory management.
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\item Use of Szczarba's formulas instead of Shih's for implementing the twisted
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Eilenberg--Zilber theorem.
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\item New mathematical objects:
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\begin{itemize}
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\item Serre spectral sequences.
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\item Differentials algebras.
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\item Simplicial morphisms.
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\item Kan simplicial sets.
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\item Simplicial groups.
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\item Fibrations.
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\item Classifying spaces.
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\end{itemize}
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In particular, using these tools, the first homotopy groups of {\em arbitrary}
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simplicial sets with effective homology, are now reachable.
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\end{enumerate}
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\par
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The present documentation is a joint work between the second and third authors.
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\cleardoublepage
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\input {kenovrvw}
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\tableofcontents
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\cleardoublepage
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\pagenumbering{arabic}
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\input {ccdoc}
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\input {ccehdoc}
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\input {homlgdoc.tex}
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\input {tprdoc}
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\input {coaldoc.tex}
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\input {aldoc.tex}
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\input {ssdoc}
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\input {smmrdoc.tex}
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\input {ezdoc.tex}
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\input {kandoc}
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\input {smgrdoc.tex}
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\input {fibrdoc.tex}
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\input {lopspdoc}
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\input {dspspdoc.tex}
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\input {lptwdoc.tex}
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\input {emspdoc1.tex}
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\input {classydoc.tex}
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\input {serredoc.tex}
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\input {cstwdoc.tex}
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\input {emspdoc2.tex}
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\input {whithdoc.tex}
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\addcontentsline{toc}{chapter}{Index}
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\printindex
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\end{document}
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