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## Higher Dimensional Kleinian Groups

My advisor says, I should invest a portion of my time, to something disjoint from my research area (= local connectedness of the boundary of relatively hyperbolic groups). Higher dimensional Kleinian groups are not exactly disjoint from that. Nevertheless they are somewhat of a different flavor. Might I say, more concrete, that the spiraling labyrinth […]

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## The invariant measure (reading / replicating parts of the paper by Levitt)

From K to L $$\mathcal{K} = \{\phi_i :A_i \to B_i \}_{i=1, … , k}$$ be a non-nesting closed system on a finite tree with at least one infinite orbit. Non nesting forces a special structure for the set of finite regular $$\mathcal{K}$$ – orbits Union of all finite regular orbits = […]

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## Protected: Tameness 1

There is no excerpt because this is a protected post.

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## Dunwoody – Day 6

A JSJ decomposition (or JSJ tree) of G over A is an A-tree T such that: T is universally elliptic; T dominates any other universally elliptic tree T’. An A-tree is universally elliptic if its edge stabilizers are elliptic in every A-tree. Recall that H is elliptic in T if it fixes a point in […]

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## Rips Machine

Let G be a finitely presented group acting minimally, stably and non trivially by isometries on an $$\mathbb{R}$$ tree S. If G does not split over an arc stabilizer of S, then one of the following is true: There is a line $$L \subset S$$ acted on by a subgroup H […]

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## Dunwoody’s accessibility theorem – Talk Day 4

This is a personal musing. Possible errors, uncredited excerpts lie ahead. We constructed sequence of equivariant maps $$f_k$$ from the universal cover $$\tilde {X}$$ to the sequence of refinements $$T_k$$. The construction was complete up to the 1-skeleton. We want to extend the maps to 2-skeleton in a certain way. To motivate the […]

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## Cut points in Bowditch Boundary of Relatively hyperbolic groups 1

This document is a personal musing. It has many excerpts without credit, potentially false claims, and misquotes. If some cosmic accident has lead you to this page, then take a deep breath and assume caution. If you are worried about copyright infringement, kindly let me know. I will modify the document. B.H. Bowditch thought about […]

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## Day 3 (notes from Craig’s Lecture)

Definition A subset N of a space X is a neighborhood of infinity if $$\bar{X /N }$$ is compact. We say that X has k ends ( $$k \in \mathbb{N} \cup \{ \infty \}$$ ) if \( k = sup \{ j | X \textrm{has a nbd of} \infty \textrm{with j […]