Homotopy theory is a cornerstone of modern algebraic topology, concerned with the study of spaces up to continuous deformations. This approach characterises topological spaces by their intrinsic ...

Type theory and homotopy theory have evolved into profoundly interconnected disciplines. Type theory, with its foundations in logic and computer science, provides a formal language for constructing ...

I am an algebraic topologist and a stable homotopy theorist. I study chromatic homotopy theory and its interactions with equivariant homotopy theory. I also work with condensed matter physicists to ...

Transactions of the American Mathematical Society, Vol. 292, No. 2 (Dec., 1985), pp. 721-732 (12 pages) ...

As topologists seek to classify shapes, the effort hinges on how to define a manifold and what it means for two of them to be equivalent. Sorting a collection of shapes is child’s play. Circles here, ...