"What is ... a van Kampen obstruction cocycle"  -- Isaac Mabillard (IST
Austria)

16:00, Friday, January 16, 2015
@TU MA 313
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ABSTRACT:
The Kuratowski theorem provides a nice criterion for graph planarity, ie,
to decide whether a simplicial 1-complex can be embedded into R^2.

A natural generalization of the problem is to find a criterion to decide
whether a simplicial n-complex K can be embedded into R^{2n}. This is what
the van Kampen obstruction cocycle gives us. By using standard tricks in
PL topology, one can show that K is embeddable if and only if (the class
of) its cocycle is zero.

This is (maybe?) surprising because embeddability is a geometric question,
whereas a cocycle is an algebraic object, but it still carries enough
information to solve the geometric problem.
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These talks are organized by students for students.

Our goal is to give you the opportunity to enhance your general
mathematical knowledge in a casual atmosphere and meet other PhD and
graduate students across the boundaries of your individual work
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