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Full-Text Articles in Physical Sciences and Mathematics
Adding Limit Points To Bass-Serre Graphs Of Groups, Alexander Jin Shumway
Adding Limit Points To Bass-Serre Graphs Of Groups, Alexander Jin Shumway
Theses and Dissertations
We give a brief overview of Bass-Serre theory and introduce a method of adding a limit point to graphs of groups. We explore a basic example of this method, and find that while the fundamental theorem of Bass-Serre theory no longer applies in this case we still recover a group action on a covering space of sorts with a subgroup isomorphic to the fundamental group of our new base space with added limit point. We also quantify how much larger the fundamental group of a graph of groups becomes after this construction, and discuss the effects of adding and identifying …
Pro-Covering Fibrations Of The Hawaiian Earring, Nickolas Brenten Callor
Pro-Covering Fibrations Of The Hawaiian Earring, Nickolas Brenten Callor
Theses and Dissertations
Let H be the Hawaiian Earring, and let H denote its fundamental group. Assume (Bi) is an inverse system of bouquets of circles whose inverse limit is H. We give an explicit bijection between finite normal covering spaces of H and finite normal covering spaces of Bi. This bijection induces a correspondence between a certain family of inverse sequences of these covering spaces. The correspondence preserves the inverse limit of these sequences, thus offering two methods of constructing the same limit. Finally, we characterize all spaces that can be obtained in this fashion as a particular type of fibrations of …