## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

 Mittagsseminar Talk Information

Date and Time: Thursday, June 22, 2006, 12:15 pm

Duration: This information is not available in the database

Location: CAB G51

Speaker: Eran Nevo (Department of Mathematics, Hebrew University)

## Combinatorial embedding obstructions for simplicial complexes

A famous result by Kuratowski asserts that a graph can be embedded into a $2$-sphere iff it contains neither of the graphs $K_5$ and $K_{3,3}$ as minors. We generalize the notion of graph minors to all (finite) simplicial complexes in a way that produces obstructions to embeddability of higher dimensional complexes in higher dimensional spheres. We make use Van Kampen's obstruction, which will be reviewed.

We answer affirmatively a problem asked by Dey et al. concerning topology-preserving edge contractions, and conclude from it the validity of the generalized lower bound inequalities for a special class of triangulated spheres.

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