Graphics Reference
In-Depth Information
Section 7.4.2
Show that the bundle (
S
n
,p) over
P
n
in Example 7.4.2.1 is locally trivial.
7.4.2.1.
7.4.2.2.
Give an intuitive justification of the fact that the lens spaces defined in Sections 7.2.4
and 7.4.2 are homeomorphic.
Section 7.4.3
7.4.3.1.
Prove Theorem 7.4.3.1.
7.4.3.2.
Prove Lemma 7.4.3.3.
Section 7.5
7.5.1.
Work through the details of a proof of Theorem 7.5.1.
7.5.2.
Work through the details of a proof of Proposition 7.5.6.
Section 7.5.1
Let f, g :
S
n
Æ
S
n
, n ≥ 1, be continuous maps.
7.5.1.1.
Prove that if f(
p
) π g(
p
) for all
p
Œ
S
n
, then
(a)
n
+
()
(
)
=
deg
f
1
deg
g
0
.
Prove that if deg f π (-1)
n+1
, then f has a fixed point.
(b)
Prove that if deg f π 1, then f(
p
) =-
p
for some
p
Œ
S
n
.
(c)
