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Presented By: RTG Seminar on Number Theory - Department of Mathematics

RTG Number Theory: Pseudo-varieties of profinite graphs and spanning trees

Amrita Acharyya (University of Toledo)

Abstract: We consider pro-C graphs for certain categories of finite graphs. After exploring some general theory, we specalize to a particular pseudo-variety denoted by ε that arises naturally in constructing end point compactifications of connected abstract graphs. We show that any connected secondcountable pro-ε graph has a profinite analogue of spanning tree as in connected abstract graphs. The structure of pro-ε graphs and their fundamental profinite groups are shown to be analogous in certain ways to that of abstract graphs and their fundamental groups.

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