"Creating 3dimensional spaces via surgery on knots and links"
Dr. Michael Williams, UCR
Wednesday, February 27, 2013
3:40–5 p.m.
Location: Surge Building 284
Parking Information
Category: Colloquium
Description: Tea @ 3:40 p.m.
Talk begins @ 4:10 p.m.
Ends @ 5:00 p.m.
Abstract:
One of the goals in 3dimensional topology is to determine whether or not two given 3dimensional spaces are topologically equivalent. The technical term for a 3dimensional space is ``3manifold". The most famous problem regarding 3manifolds is the Poincare conjecture; this conjecture was originally given as a question by Henri Poincare around 1900, and this conjecture has been proved only recently. The Poincare conjecture asserts that any closed (i.e. compact and boundaryless), simply connected 3manifold must be topologically equivalent to the 3sphere. In 1910, Max Dehn considered surgery on knots in the 3sphere as a way to construct possible counterexamples to the Poincare conjecture. Dehn was not able to find such a counterexample, but the method of surgery has proved useful to this day. An amazing theorem of Lickorish and Wallace asserts that if M is a closed, connected, orientable 3manifold, then M can be obtained by surgery on some link in the 3sphere. Much of my research centers around restricting the possible ways to create particular types of 3manifolds via surgery. In this talk, I will give a survey of the aforementioned topics while providing illustrative examples. This talk should be accessible to a general mathematical audience.
Additional Information: Math Colloquiums
Open to: General Public
Admission: Free
Sponsor: Mathematics
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