
Protected: Tameness 1
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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 […]

A survey of relative Dunwoody’s accessibility theorem
Motivation This is not (even remotely) an original work. For example it contains large excerpts from a variety of papers (often without reference). More importantly beware! What follows may contain outrageously false statements. This was created for an inclass presentation while the author was exploring these ideas for the first time.. Consider a group G […]

Accessibility
G is a finitely presented group. X is its presentation complex (a simplicial 2complex). Since G is finitely presented, the number of vertices of X is finite. Suppose \( u_1 , \cdots , u_q \) be the vertices of X. \( \tilde {X} \) be its universal cover. Fix lifts of the vertices of X. […]

Cut points in Boundary – 1
Proceedings from Top Secret Topology Seminar. Disclaimer: Handle with care. Several unproved (possibly untrue) statements lie ahead. Jump to summary. Le G be a wordhyperbolic group and \( \partial G \) its boundary. Theorem (Bestvina, Messa, 1991) If G has one end, then \( \partial G \) is connected and locally connected. The second part […]

Free Groups, Gromov Hyperbolicity – (translated excerpt from Harpe)
Soit T un arbre simplicial muni d’une distance pour laquelle chaque arête est isométrique au segment [0,1] de la droite réelle, et pour laquelle la distance entre deus points est la borne inférieure des longueurs des chemins joignant ces points. Tout triangle de T est dégénéré au sens oú chacun de ses côtés est contenu […]

The Alexander Trick
Here is the original paper: J. W. Alexander, On the deformation of an ncell (A 2page paper that influenced a remarkable amount of later work).

Ends
Motivation Start with a locally finite simplicial complex X. Locally finite: Each vertex is attached to only finitely many simplices. Why locally finite: To make sure it is a CW complex. Notice that the closurefinite criteria require each cell of a CW complex to meet only finitely many other cells. Hence we do not have a situation like […]