Artículos de revistas
Finiteness Conditions And Pdr-group Covers Of Pdn -complexes
Registro en:
Mathematische Zeitschrift. , v. 256, n. 1, p. 45 - 56, 2007.
255874
10.1007/s00209-006-0058-3
2-s2.0-33847333448
Autor
Hillman J.A.
Kochloukova D.H.
Institución
Resumen
We show that an infinite cyclic covering space M′ of a PD n -complex M is a PD n-1-complex if and only if χ(M) = 0, M′ is homotopy equivalent to a complex with finite [(n-1)/2]-skeleton and π1(M′) is finitely presentable. This is best possible in terms of minimal finiteness assumptions on the covering space. We give also a corresponding result for covering spaces M ν with covering group a PD r -group under a slightly stricter finiteness condition. © Springer-Verlag 2007. 256 1 45 56 Barge, J., Dualité dans les revêtements galoisiens (1980) Invent. Math, 58, pp. 101-106 Bieri, R., (1981) Homological Dimension of Discrete Groups, , 2nd edn. Queen Mary College Mathematics Notes, London Bieri, R., Geogeghan, R., Kernels of actions on non-positively carved spaces (1998) LMS Lecture Notes Series, 252, pp. 24-38. , Kropholler, P.H, Niblo, G.A, Stöhr, R, eds, Geometry and Cohomology in Group Theory, Cambridge University Press, Cambridge Bieri, R., Renz, B., Valuations on free resolutions and higher geometric invariants of groups (1988) Comment. Math. Helv, 63, pp. 464-497 Bieri, R., Strebel, R., Geometric Invariants for Discrete Groups, , manuscript-book, Frankfurt University in preparation Bowditch, B.H., Planar groups and the Seifert conjecture (2004) J. Reine u. Angew. Math, 576, pp. 11-62 Browder, W., Poincaré complexes, their normal fibrations and surgery (1972) Invent. Math, 17, pp. 191-202 Brown, K.S., A homological criterion for finiteness (1975) Commentarii Math. Helvetici, 50, pp. 129-135 Crisp, J.S., The decomposition of Poincaré duality complexes (2000) Commentarii Math. Helvetici, 75, pp. 232-246 Davis, M., The cohomology of a Coxeter group with group ring coefficients (1998) Duke Math. J, 91, pp. 297-314 Gottlieb, D.H., Poincaré duality and fibrations (1979) Proc. Am. Math. Soc, 76, pp. 148-150 Hillman, J.A., Four-Manifolds, Geometries and Knots (2002) Geometry Topol. Monogr, 5 Kapovich, M., (1998) On normal subgroups in the fundamental groups of complex surfaces, , preprint, University of Utah Kearton, C., An algebraic classification of some even-dimensional knots (1976) Topology, 15, pp. 363-373 Klein, J.R., The dualizing spectrum of a topological group (2001) Math. Ann, 319, pp. 421-456 Kochloukova, D.H., On a conjecture of E. Rapaport Strasser about knot-like groups and its pro-p version (2006) J. Pure Appl. Algebra, 204, pp. 536-554 Kochloukova, D.H., Some Novikov rings that are von Neumann finite and knot-like groups (2006) Comment. Math. Helv, 81, pp. 931-943 Levine, J.P., An algebraic classification of some knots of codimension two (1970) Commentarii Math. Helv, 45, pp. 185-198 Lück, W., L2-Betti numbers of mapping tori and groups (1994) Topology, 33, pp. 203-214 Mather, M., Counting homotopy types of manifolds (1965) Topology, 4, pp. 93-94 Milnor, J.W., Infinite cyclic coverings (1968) Conference on the Topology of Manifolds, pp. 115-133. , Hocking, J.G, ed, Prindle, Weber and Schmidt, Boston Ranicki, A.A., Finite domination and Novikov rings (1995) Topology, 34, pp. 619-632 Stark, C.W., Resolutions modeled on ternary trees (1996) Pacific J. Math, 173, pp. 557-569 Strebel, R., A remark on subgroups of infinite index in Poincaré duality groups Comment. Math. Helv, 52, pp. 317-324 Turaev, V.G., Three-dimensional Poincaré complexes: Classification and splitting (1989) Math. Sbornik, 180, pp. 809-830 Wall, C.T.C., Finiteness conditions for CW-complexes (1965) Ann. Math, 81, pp. 56-69