Seminara za topologiju

U okviru Seminara za topologiju u utorak 30.6. s početkom u 13:15 u predavaonici A318  

Logan Hoehn (Nipissing University, Canada) će održati predavanje pod naslovom:

Computation in continuum theory: planarity of simplicial inverse limits of graphs

Pozivaju se članovi seminara i svi zainteresirani da prisustvuju predavanju.  

Sažetak: A classic result in topology and graph theory due to Kuratowski states that a graph can be embedded in the plane

if and only if it does not contain (as a topological subspace, or alternatively, as a graph minor) either the complete

graph on 5 vertices, or the complete bipartite graph with 3 vertices on each side.

In continuum theory, specifically in the study of 1-dimensional continua, one studies spaces which can be represented as

inverse limits of sequences of connected graphs.  Among these, so-called simplicial inverse systems are common for

producing examples, and are particularly suitable to study with computational techniques.

Like with graphs, it is often important to determine whether a given continuum can be embedded in the plane or not; but

there is no forbidden substructure result analogous to Kuratowski's Theorem to rely on.  Nevertheless, there has been

recent progress towards the development of an algorithm to check planarity of a continuum which is the inverse limit of a

simplicial inverse system.

I will give an introduction to the concept of inverse limits, and discuss what is known about checking planarity of

simplicial inverse limits of graphs, and what is still missing.  I will also outline some associated computational

challenges.