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- Ross Geoghegan, Jeffrey C. Lagarias, Robert C. Melville
- SIAM Journal on Optimization
- 1998

This paper studies continuation methods for nding isolated zeros of nonlinear functions.

- ROSS GEOGHEGAN, MICHAEL L. MIHALIK, MARK SAPIR
- 2007

This paper is about geometric and topological properties of a proper CAT(0) space X which is cocompact-i.e. which has a compact generating domain with respect to the full isometry group. It is shown that geodesic segments in X can " almost " be extended to geodesic rays. A basic ingredient of the proof of this geometric statement is the topological theorem… (More)

- Ross Geoghegan, Fernando Guzm´an
- 2005

Given a set S equipped with a binary operation (we call this a " bracket algebra ") one may ask to what extent the binary operation satisfies some of the consequences of the associative law even when it is not actually associative? We define a subgroup As-soc(S) of Thompson's Group F for each bracket algebra S, and we interpret the size of Assoc(S) as… (More)

- Ross Geoghegan
- 2005

In " zero-parameter " or classical Nielsen fixed point theory one studies Fix(f) := {x ∈ X | f (x) = x} where f : X → X is a map. In case X is an oriented compact manifold and f is transverse to the identity map, id X , Fix(f) is a finite set each of whose elements carries a natural sign, ±1, the index of that fixed point. The set Fix(f) is partitioned into… (More)

- Ross Geoghegan
- 1999

In this paper we introduce the \S 1 {Euler characteristic" of a nite S 1 {space, i.e. of a topological space X with a given circle action, where X is partitioned as an \S 1 {CW complex" into nitely many \S 1 {cells" (see x4). We deene the S 1 {Euler characteristic both geometrically and as an algebraic trace and show how it ts in to the broad picture of… (More)

- Ross Geoghegan
- 1996

The relationship between xed point theory and K {theory is explained, both classical Nielsen theory (versus K 0) and 1{parameter xed point theory (versus K 1). In particular, various zeta functions associated with suspension ows are shown to come in a natural way as \traces" of \torsions" of Whitehead and Reidemeister type.

- ROSS GEOGHEGAN
- 2007

1. Geometrical results. There exist (CW) complexes X homotopy dominated by finite complexes but not homotopy equivalent to finite complexes [8] . It is unknown if there are compact metric spaces (compacta) with this property. However, one may construct a compactum, Z, shape dominated by a finite complex but not shape equivalent (hence not homotopy… (More)

- Ross Geoghegan
- 1998