Math Colloquium @ Bryn Mawr: "Where can you put a non-orientable surface?"Math Colloquium @ Bryn Mawr: "Where can you put a non-orientable surface?"http://www.haverford.edu/calendar/details/251161Bryn Mawr, Park 3282013-11-18T16:00:002013-11-18T17:00:00
November 18, 4:00PM–5:00PM
Bryn Mawr, Park 328
Daniel Ruberman (Brandeis). Bryn Mawr, Park 338.
Bi-College Math Colloquium
Where can you put a non-orientable surface?
Daniel Ruberman, Brandeis University.
Talk at 4 in Park 338
Tea at 3:30 in the Math Lounge, Park 355.
Abstract: Non-orientable surfaces are those that are one-sided, like a Möbius band or Klein bottle. While we can build a physical model of a Möbius band in 3-dimensional space, it is a theorem from algebraic topology that one cannot find a closed (meaning without boundary) non-orientable surface embedded in 3-space. But we can take advantage of the extra elbow-room to embed such a surface in 4-dimensional space. I will first describe how one can put closed non-orientable surfaces in some more complicated 3-dimensional manifolds, but not in other ones. Then I will discuss joint work with Adam Levine and Sašo Strle on the question of whether adding an extra dimension (to make a 4-dimensional manifold) can help.
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