# 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 manifold?s and bundles.

# References

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

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

category: people