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For each sheaf ${\cal F}$ with constructible cohomology,
one can associate a homology cycle $Ch({\cal F})$ called the
characteristic cycle of ${\cal F}$.
Characteristic cycles of sheaves were introduced by M.Kashiwara in 1985 and
they play an important role in algebraic geometry and representation theory.
I will give a geometric introduction to these characteristic cycles
(as opposed to the algebraic definition given by M.Kashiwara).
This will be done by describing the defining properties of characteristic
cycles which are analogous to Eilenberg-Steenrod homology axioms for homology
of topological spaces.
The talk will be very basic and I will only assume that the audience is
familiar with the notion of cohomology relative to a sheaf.
Neither perverse sheaves nor ${\cal D}$-modules will be mentioned inthis talk,
but if the sheaf ${\cal F}$ happens to be perverse,
the characteristic cycle of ${\cal F}$ equals the characteristic cycle of the
holonomic ${\cal D}$-module corresponding to ${\cal F}$ via the
Riemann-Hilbert correspondence.
The talk is based on the article by W.Schmid and K.Vilonen,
“Characteristic cycles of constructible sheaves,”
Inventiones Math. 124 (1996), 451-502.
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