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CATEGORIES:The Archimedeans (CU Mathematical Society)
SUMMARY:Handles and Homotopies - Jake Rasmussen (Cambridge
)
DTSTART;TZID=Europe/London:20191108T190000
DTEND;TZID=Europe/London:20191108T200000
UID:TALK132286AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/132286
DESCRIPTION:A k-dimensional manifold is a topological space th
at locally looks like R^k^. For example\, the surf
ace of a beach ball is a 2-dimensional manifold: i
f you cut a little piece out of it\, you can flatt
en it out so it looks like a disk in the 2-dimensi
onal plane. The surface of an inner tube (a torus)
has the same property\, so it is also a 2-manifol
d. These two spaces are locally the same (both loo
k like R^2^) but globally different. Much of what
we know about the topology of manifolds comes from
the fact that they can be decomposed into simple
pieces called handles. I'll discuss these handle d
ecompositions\, where they come from\, and some th
ings they can tell us\, both for 2-dimensional sur
faces and in higher dimensions.
LOCATION:MR2\, Centre for Mathematical Sciences
CONTACT:Valentin HÃ¼bner
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