Top onogov s Theorem and Applications
by
Wolfgang Meyer
These notes have been prepared for a series of lectures given at the College on
Di erential Geometry at Trieste in the Fall of The lectures center around To
p onogov s triangle comparison theorem critical p oint theory and applications In the
short amount of time available not all the asp ects can be covered We fo cus on those
applications which seem to be most imp ortant and at the same time most suitable
for an exp osition Some basic knowledge in geometry will be assumed It has b een
provided by K Grove in the rst series of these lectures Nevertheless we try to keep
the lectures selfcontained and indep endent as much as p ossible For the result ab out
the sum of Betti numb ers in section a lemma from algebraic top ology is needed A
pro of for this result has b een provided in the app endix
I am indebted to U Abresch for many helpful conversations and also for writing
and typing the app endix
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