ADVANCED GEOMETRY A
Geometry 1, geometry 2. It may be useful, but not essential, having attended either the course Fundamentals of Advanced Geometry, during the bachelor's degree, or Topics in Advanced Geometry, during the master's degree in mathematics
Oral exam, during which the development of some concrete example will be requested, among those treated during the lectures, and the acquired theoretical skills will be tested. More precisely some topics will be assigned to the students to be exposed in a seminar, which will involve most of the theory developed during the course and also the development of detailed proofs by the students.
EDUCATIONAL GOALS
The course aims to provide students with advanced tools for the calculation of topological invariants, with particular reference to topological or differential manifolds.
EXPECTED LEARNING ACHIEVEMENTS
the student will be able to apply the standard techniques for computation of topological invariants and to orient her/himself in the modern algebraic topology literature
Cellular complexes. Operations on spaces up to homotopy. Reviews on the fundamental group and on singular homology. Axiomatic approach to homology. Homology with coeficients in arbitrary group.
Cohomology, axiomatic approach, ring structure on cohomology. Poincaré duality. Higher homotopy groups. Explicit calculations of homotopy groups and cohomology rings.
Sketches on rational homotopy theory.
Lectures, 64 hours, which include sessions dedicated to the explicit calculation of examples.
During the course, weekly notes will be made available on e-learning.
email:
riccardo.re AT uninsubria.it
Contact the teacher via email for any clarification
Professors
Borrowers
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Degree course in: MATHEMATICS