Behavior of geodesic rays in spaces with geometric group actions.

機(jī)譯：測地線在具有幾何群動(dòng)作的空間中的行為。

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This dissertation studies certain groups by studying spaces on which they act geometrically. These spaces are studied by examining the behavior of geodesic rays in these spaces, which gives geometric data about the space that can translate into algebraic data about the group.;First, we investigate the amenability of Thompson's group F by studying the geometry of its Cayley graph. We apply the uniformly finite homology of Block and Weinberger to subsets of this graph. Many large subsets of the Cayley graph are shown to be nonamenable by exhibiting certain arrangements of geodesic rays which we call "tree-like quasi-covers".;We then examine CAT(0) boundaries. If a group acts geometrically on two CAT(0) spaces X and Y, then one obtains a G-equivariant quasi-isometry from X to Y. One may look at the image of a geodesic ray in X, and look at its closure in ∂Y. We show that this "boundary image" can have the homeomorphism type of any compact, connected subset of Euclidean space.

機(jī)譯：本文通過研究某些群體的幾何行為來研究它們。通過檢查這些空間中的測地線的行為來研究這些空間，這些行為提供了可以轉(zhuǎn)化為該組的代數(shù)數(shù)據(jù)的空間幾何數(shù)據(jù)。首先，我們通過研究湯普森F群的Cayley幾何來研究其適應(yīng)性圖形。我們將Block和Weinberger的一致有限同源性應(yīng)用于該圖的子集。通過顯示測地線的某些排列（我們稱其為“樹狀準(zhǔn)覆蓋”），顯示了Cayley圖的許多大子集是不可接受的；然后檢查CAT（0）邊界。如果一組在兩個(gè)CAT（0）空間X和Y上發(fā)生幾何作用，則一個(gè)將獲得從X到Y(jié)的G等距的等軸測圖。一個(gè)人可以查看X中測地射線的圖像，并查看X中的測地線。 ?Y。我們表明，該“邊界圖像”可以具有歐氏空間的任何緊湊的，連通的子集的同胚型。

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作者
Staley, Daniel.;
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Rutgers The State University of New Jersey - New Brunswick.;

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授予單位 Rutgers The State University of New Jersey - New Brunswick.;
學(xué)科 Mathematics.
學(xué)位 Ph.D.
年度 2010
頁碼 68 p.
總頁數(shù) 68
原文格式 PDF
正文語種 eng
中圖分類
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Behavior of geodesic rays in spaces with geometric group actions.

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