Title of Seminar: Infosys Chandrasekharan Random Geometry Colloquium
Title of Talk: Grushko decomposition theorem and Stallings Ends theorem
Speaker: Swathi Krishna, TIFR, Mumbai
Date: March 4, 2024
Time: 16:00:00 Hours
Venue: A-369
Abstract: In Bass Serre theory, we saw that if a finitely generated group acts on a tree without inversion of edges, it has a graph of groups structure. If the edge groups are trivial, the group is a free product. If a group cannot be expressed as a free product, it is said to be freely indecomposable. In this talk, we will first look at Grushko decomposition theorem, which expresses a finitely generated group as a free product of finitely many freely indecomposable groups. In the next step, to study if a freely indecomposable group can be expressed as either an amalgamated free product or an HNN extension over a finite group, we have the notion of 'ends'. We will look at some examples and results relating ends of a finitely generated group and its splitting, including Stallings ends theorem. We will end with some applications if time permits.
Title of Talk: Grushko decomposition theorem and Stallings Ends theorem
Speaker: Swathi Krishna, TIFR, Mumbai
Date: March 4, 2024
Time: 16:00:00 Hours
Venue: A-369
Abstract: In Bass Serre theory, we saw that if a finitely generated group acts on a tree without inversion of edges, it has a graph of groups structure. If the edge groups are trivial, the group is a free product. If a group cannot be expressed as a free product, it is said to be freely indecomposable. In this talk, we will first look at Grushko decomposition theorem, which expresses a finitely generated group as a free product of finitely many freely indecomposable groups. In the next step, to study if a freely indecomposable group can be expressed as either an amalgamated free product or an HNN extension over a finite group, we have the notion of 'ends'. We will look at some examples and results relating ends of a finitely generated group and its splitting, including Stallings ends theorem. We will end with some applications if time permits.