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.