# Colloquium: Mathematical Surgery (Friday)

Come see your fellow undergrad Alec Leng (’21) give a talk on knot theory this Friday afternoon. See below for details and Alec’s summary of the talk.

Since this is a new kind of event, please take 10 seconds to tell me if you are thinking about attending! I want to make sure we have plenty of food.
Who: Alec Leng (’21)
What? An Introduction to (Mathematical) Surgery
When? Friday, April 5, 4:30-5:15 pm
Where? Fine 214
Food? Jules Pizza (pls email me if you have suggestions for toppings)
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Consider a topological circle:

Now let’s cut out part of it:

Rotate,

And stick it back in!

And now we have two circles! Stated a bit more technically, we’ve cut out a copy of S^0xD^1 from S^1, and then glued it back in a different way to produce two S^1s. This process is called surgery, and one can do it on general manifolds as well; in particular, it lets us generate a lot of 3 dimensional manifolds! Come to this talk to see more (hopefully somewhat pretty) pictures, more examples of surgery, and hear about why it’s such a vital tool in geometric topology.
I’ll be assuming some basic topology (e.g. intuitive definition of a manifold, idea of what a homeomorphism is, and ideally being able to visualize S^3 as 3 dimensional Eucildean space but with an extra point, though don’t worry if you can’t— I’ll talk more about this at the beginning of my talk).

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Hope to see you there!!
Sincerely,