nLab
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

  • 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.

Selected writings

On homotopy theory and the Adams conjecture:

  • Dennis Sullivan, Genetics of homotopy theory and the Adams conjecture, Annals of Math., 100, (1974), 1–79.

On rational homotopy theory:

  • Dennis Sullivan, Infinitesimal computations in topology, Publications mathématiques de l’ I.H.É.S. 47 (1977) 269-331, numdam, pdf

On Sullivan models for free loop spaces:

On the statement that the co-binary Sullivan differential is the dual Whitehead product:

category: people

Last revised on October 7, 2019 at 01:24:32. See the history of this page for a list of all contributions to it.