This webpage hosts software on the problem of determining the possible isotropy weights of Hamiltonian circle actions with a minimal number of fixed points.

All algorithms used are based on the paper:

*New Tools for Classifying Hamiltonian Circle Actions with Isolated Fixed Points*

Authors: Leonor Godinho, Silvia Sabatini

Paper: pdf

In particular, it determines all possible isotropy weights for actions that satisfy a certain “Positivity Condition”. This condition is satisfied, for example, by all Hamiltonian circle actions with a minimal number of fixed points on manifolds of dimension 4 or 6. When the dimension is 8, it is satisfied by all such circle actions that extend to a 2-torus action and by actions that do not have any isotropy weight equal to 1. Note that there are no known examples of Hamiltonian circle actions with a minimal number of fixed points that do not satisfy this condition.

The necessary files for any dimension can be downloaded from the link “General Files” above. The resulting files for dimensions 4, 6 and 8 can also be downloaded from the corresponding links above.