Adding Limit Points to Bass-Serre Graphs of Groups
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 s...
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| Format: | Others |
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BYU ScholarsArchive
2018
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| Online Access: | https://scholarsarchive.byu.edu/etd/6954 https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=7954&context=etd |
| Summary: | 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. |
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