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\begin{document}

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\section*{Dennis Sullivan}

Dennis Sullivan is an American topologist. His initial work was in geometric topology, but later he developed theories of localisation of homotopy types, rational homotopy theory, and aspects of string topology.

The editor ([[Andrew Ranicki]]) of the redistribution of his 1970 notes wrote:

The notes had a major influence on the development of both algebraic and geometric topology, pioneering

\begin{itemize}%
\item the localization and completion of spaces in homotopy theory, including p-local, profinite and rational homotopy theory, leading to the solution of the [[Adams conjecture]] on the relationship between vector bundles and spherical fibrations,


\item the formulation of the `Sullivan conjecture' on the contractibility of the space of maps from the classifying space of a finite group to a finite dimensional CW complex,


\item the action of the Galois group of $\overline{\mathbb{Q}}$ over $\mathbb{Q}$ on smooth manifold structures in profinite homotopy theory,


\item the K-theory orientation of [[PL manifold]]s and bundles.



\end{itemize}
\hypertarget{external_links}{}\subsection*{{External links}}\label{external_links}

\begin{itemize}%
\item \href{http://www.math.sunysb.edu/~dennis/}{website}


\item \href{http://en.wikipedia.org/wiki/Dennis_Sullivan}{Wikipedia entry}


\item interview by [[Kathryn Hess]]: \href{https://www.youtube.com/watch?v=K8kPS6FZBoc&feature=youtu.be}{video}



\end{itemize}
\hypertarget{selected_writings}{}\subsection*{{Selected writings}}\label{selected_writings}

\begin{itemize}%
\item Dennis Sullivan, \href{http://www.maths.ed.ac.uk/~aar/books/gtop.pdf}{Geometric Topology: Localization, Periodicity, and Galois Symmetry (The 1970 MIT notes)}

\end{itemize}
On [[homotopy theory]] and the [[Adams conjecture]]:

\begin{itemize}%
\item Dennis Sullivan, \emph{Genetics of homotopy theory and the Adams conjecture}, Annals of Math., 100, (1974), 1--79.

\end{itemize}
On [[rational homotopy theory]]:

\begin{itemize}%
\item Dennis Sullivan, \emph{Infinitesimal computations in topology,} Publications math\'e{}matiques de l' I.H.\'E{}.S. \textbf{47} (1977) 269-331, \href{http://www.numdam.org/item?id=PMIHES_1977__47__269_0}{numdam}, \href{http://archive.numdam.org/ARCHIVE/PMIHES/PMIHES_1977__47_/PMIHES_1977__47__269_0/PMIHES_1977__47__269_0.pdf}{pdf}

\end{itemize}
On [[Sullivan models for free loop spaces]]:

\begin{itemize}%
\item [[Micheline Vigué-Poirrier]], [[Dennis Sullivan]], \emph{The homology theory of the closed geodesic problem}, J. Differential Geometry 11 (1976) 633-644.

\end{itemize}
On the statement that \emph{[[the co-binary Sullivan differential is the dual Whitehead product]]}:

\begin{itemize}%
\item [[Pierre Deligne]], [[Phillip Griffiths]], [[John Morgan]], [[Dennis Sullivan]], \emph{Real homotopy theory of Kähler manifolds}, Invent Math (1975) 29: 245 (\href{https://doi.org/10.1007/BF01389853}{doi:10.1007/BF01389853})

\end{itemize}
\hypertarget{related_lab_entries}{}\subsection*{{related $n$Lab entries}}\label{related_lab_entries}

\begin{itemize}%
\item [[rational homotopy theory]]


\item [[Sullivan conjecture]]


\item [[model structure on dg-algebras]]


\item [[string topology]]


\item [[Simons-Sullivan structured bundle]]


\item [[Whitehead product]], [[the co-binary Sullivan differential is the dual Whitehead product]]



\end{itemize}
category: people

[[!redirects D. Sullivan]] [[!redirects Sullivan]]



\end{document}