IAS/Park City Mathematics Series
Volume 7, 1999Euler Characteristics and
Lagrangian Intersections
Mikhail Grinberg and Robert MacPhersont
Introduction
This paper is a close transcript of the lectures given by the senior author at the
Park City Mathematics Institute in July 97. Our goal is to give an introduction
to the microlocal point of view on constructible sheaves. The word "sheaf" does
not appear in the main body of the paper (except in the last section, as a part
of "perverse sheaf"). In the first three lectures we only discuss sheaf theory on
the level of Euler characteristics. For this, we need not talk about sheaves, but
only about constructible functions. In Lectures 4 and 5 we introduce Fa.ry functors
and perverse sheaves. The definitions we give are an alternative to the standard
definitions of sheaf theory. To our knowledge, they have not previously appeared in
print (see, however, [MP]). Along the way, we discuss the main notions of stratified
Morse theory: Whitney stratifications, conormal varieties, the characteristic cycle,
Morse data, etc. We preserve the informal style of the original lectures, leaving
many important facts as exercises. The reader interested in pursuing the subject
further is referred to the monographs [GM] and [KS].
(^1) Department of Mathematics, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139.
t School of Mathematics, Institute for Advanced Study, Olden Lane, Princeton, NJ 08540.
E-mail address: grinberg©math.mi t. edu trdm©math. ias. edu.
@1999 American Mathematical Society267