nLab
orbit type

Contents

Contents

Idea

In discussion of topological G-spaces (such as in equivariant homotopy theory and/or equivariant differential topology) by an orbit type one means the isomorphism class of orbits of the equivariance group.

Since every orbit of a group GG (typically taken to be a topological group) is isomorphic, as a topological G-space, to a coset space G/HG/H, and since these coset spaces, in turn, are isomorphic to each other precisely if the subgroups HH are conjugate to each other (see also at orbit category), the GG-orbit types are often identified with the conjugacy classes (H)(H) of the subgroups of GG.

References

Last revised on April 8, 2021 at 01:55:38. See the history of this page for a list of all contributions to it.