## a van Kampen obstruction cocycle?

Who?
Isaac Mabillard (Institute of Science and Technology Austria)
When?
2015/01/16, 16:00
Where?
TU Berlin, at room MA313 (Straße des 17. Juni 136)
The Kuratowski theorem provides a nice criterion for graph planarity, ie, to decide whether a simplicial $1$-complex can be embedded into $\mathbb{R}^2$.
A natural generalization of the problem is to find a criterion to decide whether a simplicial $n$-complex $K$ can be embedded into $\mathbb{R}^{2n}$. 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.