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

"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

groups.

### Time & Location

Jan 16, 2015 | 04:00 PM