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(a)
(b)
(c)
Figure 8.4:
(a) A manifold
M
and three lower level sets
M
a
,
M
b
,
M
c
, with respect to the height
function. (b) ere are no critical points in f
1
.a;b/: M
a
(left) and M
b
(right) are diffeomorphic.
(c) e passage through the critical point
p
of index
1
causes a topological change:
M
c
(left) has the
same homotopy type as
M
b
with a
1
-cell attached (right) [
24
].
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