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

Speaker:

Cabral Balreira

Title:

Global Injectivity as a Topological Phenomenon

Abstract:

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.


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