2nd module

A.A. 1998/99

Prof. Edoardo Ballico

PROGRAMME

The course is divided into 3 parts which are the natural continuations of 3 topics I introduced in my previous courses Geometria II and Ististuzioni di Geometria Superiore, first part. The examination will consists of an oral examination on two of these topics choosen freely by each student. Students with a different background (for instance Erasmus/Socrates students) without any background on one of these topics, may choose to take the examination only on this topic, starting from the very beginning and going on up to the end.
 

Topic A) Riemannian Geometry: Connections, Riemannian manifolds, Gauss curvature, complete Riemannian Manifolds and geodesic convexity. Textbook: L. Conlon " Differentiable Manifold, A first Course, BirkhŠuser Advanced Texts, 1993,  Chapter 10, sections 1, 2, 3, 4, 5.
Topic B) Holomorphic functions of several complex variables.
Topic C). Some topics in Algebraic Topology: Fundamental group, coverings, CW-complexes and singular cohomology. For the first two arguments I will follow M. Greenberg, " Lectures on Algebraic Topology ", W. A. Benjamin, 1971, Part I, e C. De Fabritiis - C. Petronio " Esercizi svolti e complementi di topologia e geometria ", Bollati Boringhieri, chapter 2; for the last two topics I will follow W. S. Massey,  Singular Homology Theory, Graduate Text. in Math. 70, Springer-Verlag, chapters 4 e 7 and a very small part of chapters 5 and 6.