![0708-1300-ClassPhoto.jpg](/images/thumb/d/d4/0708-1300-ClassPhoto.jpg/215px-0708-1300-ClassPhoto.jpg) Add your name / see who's in!
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Week of...
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Links
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Fall Semester
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1
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Sep 10
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About, Tue, Thu
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2
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Sep 17
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Tue, HW1, Thu
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3
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Sep 24
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Tue, Photo, Thu
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4
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Oct 1
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Questionnaire, Tue, HW2, Thu
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5
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Oct 8
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Thanksgiving, Tue, Thu
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6
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Oct 15
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Tue, HW3, Thu
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7
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Oct 22
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Tue, Thu
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8
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Oct 29
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Tue, HW4, Thu, Hilbert sphere
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9
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Nov 5
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Tue,Thu, TE1
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10
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Nov 12
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Tue, Thu
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11
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Nov 19
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Tue, Thu, HW5
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12
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Nov 26
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Tue, Thu
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13
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Dec 3
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Tue, Thu, HW6
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Spring Semester
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14
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Jan 7
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Tue, Thu, HW7
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15
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Jan 14
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Tue, Thu
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16
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Jan 21
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Tue, Thu, HW8
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17
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Jan 28
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Tue, Thu
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18
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Feb 4
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Tue
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19
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Feb 11
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TE2, Tue, HW9, Thu, Feb 17: last chance to drop class
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R
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Feb 18
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Reading week
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20
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Feb 25
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Tue, Thu, HW10
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21
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Mar 3
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Tue, Thu
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22
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Mar 10
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Tue, Thu, HW11
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23
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Mar 17
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Tue, Thu
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24
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Mar 24
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Tue, HW12, Thu
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25
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Mar 31
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Referendum,Tue, Thu
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26
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Apr 7
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Tue, Thu
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R
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Apr 14
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Office hours
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R
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Apr 21
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Office hours
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F
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Apr 28
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Office hours, Final (Fri, May 2)
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Register of Good Deeds
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Errata to Bredon's Book
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Announcements go here
In Preparation
The information below is preliminary and cannot be trusted! (v)
Today's Agenda
Debts
A bit more about proper functions on locally compact spaces.
Smooth Retracts and Smooth Brouwer
Theorem. There does not exist a smooth retract
.
Corollary. (The Brouwer Fixed Point Theorem) Every smooth
has a fixed point.
Suggestion for a good deed. Tell Dror if he likes the Brouwer fixed point theorem, for he is honestly unsure. But first hear some drorpaganda on what he likes and what he doesn't quite.
Corollary. The sphere
is not smoothly contractible.
Challenge. Remove the word "smooth" everywhere above.
Smooth Approximation
Theorem. Let
be a closed subset of a smooth manifold
, let
be a continuous function whose restriction
to
is smooth, and let
be your favourite small number. Then there exists a smooth
so that
and
. Furthermore,
and
are homotopic via an
-small homotopy.
Theorem. The same, with the target space replaced by an arbitrary compact metrized manifold
.
Tubular Neighborhoods
Theorem. Every compact smooth submanifold
of
has a "tubular neighborhood".