homotopy theory

The general theme of his career has been abstract homotopy theory.

This can be formulated in terms of homotopy theory.

In homotopy theory terms, the circle and the complex plane without its origin are equivalent.

In the 1950s, homotopy theory was at an early stage of development, and unsolved problems abounded.

This leads to the idea of using multiple groupoid objects in homotopy theory.

In mathematics, the Puppe sequence is a construction of homotopy theory.

The Whitehead product is an operation in homotopy theory.

There are others, coming from stable homotopy theory.

The convergence is to groups in stable homotopy theory, about which information is hard to come by.

Ravenel's main area of work is stable homotopy theory.

This was the origin of simple homotopy theory.

The homotopy theory is deeply related to the stability of topological defects.

He has made many other contributions to homotopy theory in the past four decades, including an approach to infinite loop spaces.

A parallel development, speaking in fact the same language, was that of spectrum in homotopy theory.

This concept is important in homotopy theory and in theory of model categories.

The standard textbook on rational homotopy theory is .

This connection established the deep interest of the cohomology operations for homotopy theory, and has been a research topic ever since.

He was also an architect (along with Dennis Sullivan) of rational homotopy theory.

He introduced the idea of simple homotopy theory, which was later much developed in connection with algebraic K-theory.

Thus, in terms of the homotopy theory of , these maps are interchangeable.

This accounts for much of the importance of loop spaces in stable homotopy theory.

Unlike the other characteristic classes, the Euler class is unstable, in the sense of stable homotopy theory.

He also identified the compact-open topology on function spaces as being particularly appropriate for homotopy theory.

Hopkins' work concentrates on algebraic topology, especially stable homotopy theory.

They include examples drawing on homotopy theory (classifying toposes).