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Lectures on Point Residues, Márcio G. Soares
Throughout these notes we will sometimes refer, without proof, to results on Differential Topology, Commutative Algebra, Several Complex Variables and Algebraic Topology. In each section we quote basic references on these subjects and we urge the reader, in case he (she) is not familiarized with them, to have this bibliography at hand.
Contents: Introduction, 1, Abrief view of Cauchy?s theory, Index of a point relative to a path, Holomorphic functions, Meromorphic functions,
2. The index and the multiplicity, The Poincaré Hopf index, The Brouwer degree, Holomorphic maps, The index, The Milnor number, First results on the multiplicity, The preparation theorem,
3. Grothendieck residues, The trace map, The residue, Local duality,
4. Residues and kernels, Complex valued differential forms, Volume forms and the Hodge *--operator, The Bochner-Martinelli kernel, Dolbeault cohomology.