## FSU Topology Week

Title: UV^k Mappings

Speaker: John Bryant (Florida State University, Emeritus Professor)

Abstract: In 1890 Giuseppe Peano discovered a way to continuously map the unit interval onto the square. Some 65 years later Lyudmila Keldysh showed that there are continuous, dimension-raising maps defined on the 3-cube having connected point-inverses. In this talk, which is based on joint work with Steve Ferry and Washington Mio, we discuss ways in which Keldysh's result can be generalized. In particular, we describe conditions under which a map $f\colon X \to Y$ is homotopic to a $UV^k$-mapping; that is, a surjection with $k$-connected point-inverses.