Equivariant Knots and Real Monopoles

Equivariant knots are knots equipped with a specified symmetry. Extending this notion, one can define equivariant Seifert surfaces in S^3 and equivariant slice surfaces in D^4. However, even the equivariant Seifert genus is difficult to determine, as there is no analogue of the classical Seifert algorithm for equivariant knots. In this talk, I will discuss work in progress that uses invariants from the real monopole Floer homotopy type to obtain lower bounds for the equivariant slice genus. A potentially interesting application is a bound on the equivariant Seifert genus for certain Montesinos knots. This is a joint work with Jin Miyazawa.