nLab
orthogonal calculus

Contents

Idea

The orthogonal calculus is a calculus of functors from vector spaces to homotopy types, similar to but different from the Goodwillie calculus of (infinity,1)-functors.

The prime example is the assignment VBO(V)V \mapsto B O(V) of the classifying space of the orthogonal group O(V)O(V) to any inner product vector space VV. In this example, and in general, first derivatives in the orthogonal calculus reproduce and generalize much of the theory of Stiefel-Whitney classes?. Similarly, second derivatives in the orthogonal calculus reproduce and generalize much of the theory of Pontryagin classes. (see Weiss 95)

The complex analog of the orthogonal calculus is known as the unitary calculus.

References

Last revised on October 18, 2016 at 09:17:03. See the history of this page for a list of all contributions to it.