 
Summary: Mathematics 241A
Introduction to Global Analysis
John Douglas Moore
Department of Mathematics
University of California
Santa Barbara, CA, USA 93106
email: moore@math.ucsb.edu
Fall, 2010
Preface
These are slightly revised lecture notes for the graduate course, Topics in Ge
ometry, given at UCSB during the fall quarter of 2009. We intend to include
additional topics later. It might be helpful to start with an overview of the
subject presented.
Morse theory might have developed in three main stages, although as events
transpired, the three stages were actually intertwined.
The first stage should have been finitedimensional Morse theory, which re
lates critical points of proper nonnegative functions on finitedimensional man
ifolds to the topology of these manifolds. Indeed, the foundations for this were
laid in Marston Morse's first landmark article on Morse theory [55], but he
quickly turned his attention to problems from the calculus of variations, which
