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
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,
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,
the action of the Galois group of $\overline{\mathbb{Q}}$ over $\mathbb{Q}$ on smooth manifold structures in profinite homotopy theory,
the K-theory orientation of PL manifolds and bundles.
interview by Kathryn Hess: video
On localization in homotopy theory:
Introducing string topology:
Moira Chas, Dennis Sullivan, String topology, Ann. Math. math.GT/9911159
Ralph Cohen, John R. Klein, Dennis Sullivan, The homotopy invariance of the string topology loop product and string bracket, J. of Topology 2008 1(2):391-408; doi
Exposition of the perspective of regarding string topology-operations as the TQFT of a topological string sigma model:
Dennis Sullivan, Sigma models and string topology, in: Mikhail Lyubich, Leon Takhtajan (eds.), Graphs and Patterns in Mathematics and Theoretical Physics, Proc. Symp. Pure Math. 73 (2005) (doi:10.1090/pspum/073, spire:1697823)
Dennis Sullivan, Open and closed string field theory interpreted in classical algebraic topology, chapter 11 in: Ulrike Tillmann (ed.) Topology, Geometry and Quantum Field Theory, Cambridge University Press (2005) (doi:10.1017/CBO9780511526398.014)
On homotopy theory and the Adams conjecture:
On Sullivan models for free loop spaces:
On the statement that the co-binary Sullivan differential is the dual Whitehead product:
Last revised on January 10, 2020 at 10:37:17. See the history of this page for a list of all contributions to it.