Master thesis on Rational Homotopy Theory
https://github.com/Jaxan/Rational-Homotopy-Theory
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36 lines
1.2 KiB
36 lines
1.2 KiB
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\chapter{Homotopy Theory For cdga's}
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Recall the following facts about cdga's over a ring $\k$:
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\begin{itemize}
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\item A map $f: A \to B$ in $\CDGA_\k$ is a \emph{quasi isomorphism} if it induces isomorphisms in cohomology.
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\item The finite coproduct in $\CDGA_\k$ is the (graded) tensor products.
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\item The finite product in $\CDGA_\k$ is the cartesian product (with pointwise operations).
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\item The equalizer (resp. coequalizer) of $f$ and $g$ is given by the kernel (resp. cokernel) of $f - g$. Together with the (co)products this defines pullbacks and pushouts.
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\item $\k$ and $0$ are the initial and final object.
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\end{itemize}
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In this chapter the ring $\k$ is assumed to be a field of characteristic zero.
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\section{Cochain models for the $n$-disk and $n$-sphere}
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\input{notes/CDGA_Basic_Examples}
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\section{The Quillen model structure on \titleCDGA}
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\input{notes/Model_Of_CDGA}
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\section{Homotopy relations on \titleCDGA}
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\input{notes/Homotopy_Relations_CDGA}
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\chapter{Polynomial Forms}
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\label{sec:cdga-of-polynomials}
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\section{CDGA of Polynomials}
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\input{notes/CDGA_Of_Polynomials}
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\section{Polynomial Forms on a Space}
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\label{sec:polynomial-forms}
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\input{notes/Polynomial_Forms}
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\input{notes/Minimal_Models}
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\input{notes/A_K_Quillen_Pair}
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