# Seminar za konačnu matematiku

lokacija:
Fakultet za matematiku Sveučilišta u Rijeci
vrijeme:
13.06.2024 - 12:15 - 14:00

četvrtak,13.6.2024. u 12:15 sati u predavaonici O-027 Fakulteta za matematiku Sveučilišta u Rijeci, Radmile Matejčić 2, Rijeka, na Seminaru za konačnu matematiku Boris Zgrablić, University of Primorska, FAMNIT, održat će dva predavanja:

12:15 – 13:00     Coverings of general digraphs
13:15 – 14:00     Coverings of Graphoids: Existence Theorem and Decomposition Theorems

Pozivaju se članovi Seminara i svi zainteresirani.

Sažetci predavanja:

12:15 – 13:00      Coverings of general digraphs

ABSTRACT:
A unified theory of covering projections of graphs and digraphs is presented as one theory by considering coverings of general digraphs, where multiple directed and undirected edges together with oriented and unoriented loops and semiedges, are allowed. Coverings of general digraphs can display certain unusual behaviour since the naturally defined projections of their underlying graphs may not be coverings in the usual topological sense. Consequently, homotopy does not always lift, although the unique walk lifting property still holds. It is still possible to approach such coverings algebraically in terms of the action of the fundamental monoid, and study them combinatorially in terms of voltages. We will address the problem of lifting automorphisms and give relevant results.

This is a joint work with Aleksander Malnič.

PUBLICATION:
Aleksander Malnič, Boris Zgrablić. Coverings of general digraphs.
Accepted for publication in Ars Math. Contemp.

13:15 – 14:00     Coverings of Graphoids: Existence Theorem and Decomposition Theorems

ABSTRACT:
A graphoid or general graph is a mixed multigraph with multiple directed and/or undirected edges, loops, and semiedges. A covering projection of graphoids is an onto mapping between two graphoids such that at each vertex, the mapping restricts to a local bijection on incoming edges and outgoing edges. The existence theorem for covering projections is formulated in terms of the action of the fundamental monoid. A more conventional formulation in terms of the weak fundamental group is possible because the action of the fundamental monoid is permutational. The standard formulation in terms of the fundamental group holds for a restricted class of coverings, called homogeneous. We will address the existence of the universal covering and the problems related to decomposing regular coverings via regular coverings and give relevant results.

This is a joint work with Aleksander Malnič.

PUBLICATION:
Aleksander Malnič, Boris Zgrablić. Coverings of Graphoids: Existence Theorem and Decomposition Theorems.
Symmetry 2024, 16, 375. https://doi.org/10.3390/sym16030375