Seminar za topologiju
lokacija:
PMF Matematički odsjek
vrijeme:
30.06.2026 - 13:15 - 15:00
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.
