Abstract
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 together such limit points in more general graphs of groups. We conclude with a theorem stating that the cokernel of the map on fundamental groups induced by collapsing an arc between two limit points contains a certain fundamental group of a double cone of graphs of groups, and we conjecture that this cokernel is isomorphic to this double cone group.
Degree
MS
College and Department
Physical and Mathematical Sciences; Mathematics
Rights
http://lib.byu.edu/about/copyright/
BYU ScholarsArchive Citation
Shumway, Alexander Jin, "Adding Limit Points to Bass-Serre Graphs of Groups" (2018). Theses and Dissertations. 6954.
https://scholarsarchive.byu.edu/etd/6954
Date Submitted
2018-07-01
Document Type
Thesis
Handle
http://hdl.lib.byu.edu/1877/etd10245
Keywords
covering space, inverse limit, Bass-Serre
Language
english