Y-algebra generated by the hyperbolic plane, as drawn by Bill Thurston.

Topology is the qualitative study of shapes and spaces by identifying and analyzing features that are unchanged when the object is continuously deformed — a “search for adjectives,” as Bill Thurston put it.

Topology took off at Cornell thanks to Paul Olum who joined the faculty in 1949 and built up a group including Israel Berstein, William Browder, Peter Hilton, and Roger Livesay. Together they founded the Cornell Topology Festival in 1962, which continues to be an annual event.

In the 1960s Cornell's topologists focused on algebraic topology, geometric topology, and connections with differential geometry. More recently, the interests of the group have also included low-dimensional topology, symplectic geometry, the geometric and combinatorial study of discrete groups, and dynamical systems.

Field Members

Algebraic geometry, homological algebra, mathematical physics, and representation theory
Symplectic geometry
Combinatorial group theory
Geometric group theory, geometric topology
Geometric group theory
Geometric topology, infinite-dimensional topology
Algebraic topology and algebraic K-theory

Emeritus and Other Faculty

Algebra, topology, group theory
Topology, geometric (combinatorial) group theory
Topological combinatorics and convex geometry
Geometric topology
Algebra, number theory, algebraic and differential topology
Symplectic geometry: group actions on manifolds, pseudo-holomorphic curves, and model theory.
Differential topology, group actions
Topology, geometric group theory

Activities and Resources