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SOME DEVELOPMENTS IN NIELSEN FIXED POINT THEORY
JIANG, BOJU TOPOLOGY AND GEOMETRY RESEARCH CENTER 1994 Proceedings of the Topology and Geometry Research Vol.5 No.-
Motivated by dynamical systems theory, new questions are being discussed about fixed points and periodic orbits of surface homeomorphisms. This article is an exposition of this line of research. Topics include generalized Lefschetz zeta function, asymptotic Nielsen number, linking of periodic orbits, minimal set of periods, etc.
Gross, Jonathan L. TOPOLOGY AND GEOMETRY RESEARCH CENTER 1993 Proceedings of the Topology and Geometry Research Vol.4 No.1
Generalizing the four-color problem for planar maps in 1890 into the Heawood problem for arbitrary closed surfaces provided an outstanding mathematical problem, whose complete solution required until 1968. After briefly sketching the methods of topological graph theory related to this classical investigation, we survey five programmatic themes prevalent in recent and on-going research. One such theme is a full-fledged analysis of extreme imbeddings, involving mainstream algorithmic techniques, the computation of bounds, and a theory of obstructions. A second is enumerative analysis of imbedding distributions and covering-space constructions. A third is statistical analysis of imbedding distributions, originally motivated by the problem of graph isomorphism testing. A fourth is applications to computer science, for instance, to the theory of parallel processor interconnection networks. A fifth is generalization of the domain and range types for imbeddings, for instance, with 2-complexes as domains or with 3-space as the range. A list of some suggested research problems is provided .
FIXED POINTS THEORY ON GEOMETRIC SEIFERT MANIFOLDS
Kang, Eun Sook,Lee, Kyung Bai TOPOLOGY AND GEOMETRY RESEARCH CENTER 1997 Proceedings of the Topology and Geometry Research Vol.8 No.-
We Study fixed point of isometries on 3-manifolds M with one of the 6 Seifert geometries. For each isometry ?: M → M, we determine the Lefschetz number L(?) and the Nielsen number N(?).
AMENABILITY AND RIGIDITY OF A MANIFOLD
PAENG, SEONG-HUN TOPOLOGY AND GEOMETRY RESEARCH CENTER 1999 Proceedings of the Topology and Geometry Research Vol.10 No.-
Using asymptotic geometry, we study the regidity of the fundametal group of a compact Riemannian manifold M.
GOLDMAN, WILLIAM M. TOPOLOGY AND GEOMETRY RESEARCH CENTER 1994 Proceedings of the Topology and Geometry Research Vol.5 No.-
This article summarizes a series of 3 90-minute talks presented at the joint TGRC-KOSEF workshop held at Kyungpook National University in Taegu on July 4-8, 1994. Most of the material I discussed may be found in the survey article, "Complex hyperbolic Kleinian groups," (published in "Complex Geometry," Proceedings of the Osaka International Conference, Marcel Dekker, pp. 31-52 (1992)), and my forthcoming book, "Complex Hyperbolic Geometry," (accepted for publication by Oxford Mathematical Monographs, Oxford University Press). I see no need to duplicate material already available in the literature. Furthermore a more informal and intuitive treatment of this materials may be valuable. For that reason I outline my lectures from the workshop, referring to the Osaka survey article and the monograph for details.