Introduction to
(smooth) Manifolds
Manifolds, the higher-dimensional analogs of smooth curves and
surfaces, are fundamental objects in modern mathematics. Combining
aspects of algebra, topology, and analysis, manifolds have also been
applied to classical mechanics, general relativity, and quantum
field theory. The aim of this course is to get aquainted with the
basic theory and lots of examples of manifolds. Towards the end of
the course we will learn to compute, at least for simple spaces, one
of the most basic topological invariants of a manifold, its de Rham
cohomology.
Syllabus
Line arrangements and some classical problems, posets and
Mobius inversion, hyperplane arrangements,
deletion-restriction, Zaslavsky's theorem, graphical
arrangements, matroids, the finite field method, ESA, interval
order, Shi and Catalan arrangements, free arrangements.