Ty Ghaswala, Department of Pure Mathematics, University of Waterloo
“Dot dash dash dot. Dot dot dash. Dash dot.”
We
will
continue
working
through
Milnor's
Morse
theory,
and
this
week
we
will
be
going
through
theorem
3.5.
Given
a
manifold
$M$
and
a
function
$f:M
\to
\mathbb{R}$,
this
theorem
gives
us
an
explicit
cell
decomposition
of
$M$
in
terms
of
the
indices
of
the
critical
points
of
$f$.
Time
permitting,
we
will
see
our
work
beating
through
the
technical
results
over
the
last
few
weeks
come
to
fruition
with
some
very
cool
applications.