Graduate Student Seminar, 4:30 pm December 6, 2004; HH127


Cabral Balreira


Global Injectivity as a Topological Phenomenon


We consider the problem of finding conditions under which a locally invertible map has a global inverse. We begin with Hadamard's theorem which states that properness is a necessary and sufficient condition to obtain an inverse. We will investigate the complex case and state a result of Nollet and Xavier on holomorphic injectivity and the Hopf map. Finally, we will observe that connectedness is a key issue in proving injectivity.

To volunteer to give a talk, or for any other questions regarding this schedule, contact Sara Miller