Freedman, Michael H. A geometric reformulation of 4-dimensional surgery. (English) Zbl 0898.57005 Topology Appl. 24, No. 1-3, 133-141 (1986). Summary: Certain topological generalizations of the Schottky groups are described. These act on the three spheres. The question of finding a suitable extension over \(B^4\) is considered and shown to be equivalent to the topological surgery-conjecture. The high-dimensional analogues of these actions are shown to have suitable extensions. Cited in 2 ReviewsCited in 9 Documents MSC: 57N13 Topology of the Euclidean \(4\)-space, \(4\)-manifolds (MSC2010) 57N70 Cobordism and concordance in topological manifolds 57S25 Groups acting on specific manifolds 57R80 \(h\)- and \(s\)-cobordism Keywords:limit sets; group actions; Schottky group PDFBibTeX XMLCite \textit{M. H. Freedman}, Topology Appl. 24, 133--141 (1986; Zbl 0898.57005) Full Text: DOI References: [1] Bing, R. H., A homeomorphism between the 3-sphere and the sum of two solid horned spheres, Ann. Math., 56, 354-362 (1952) · Zbl 0049.40401 [2] Casson, A.; Freedman, M., Atomic surgery problems, Contemp. Math., 35, 181-199 (1984) [3] Freedman, M. H., The topology of four-dimensional manifolds, J. Diff. Geom., 17, 357-453 (1982) · Zbl 0528.57011 [4] Freedman, M. H., Proc. Internat. Congress Math., Warsaw, Poland. Proc. Internat. Congress Math., Warsaw, Poland, The disk theorem for four-dimensional manifolds (1983) [5] Freedman, M. H., A new technique for the link slice problem, Invent. Math. (1985), to appear. · Zbl 0569.57002 [6] Freedman, M. H.; Skora, R., Strange actions of free groups on spheres, J. Diff. Geom. (1986), to appear. [7] Kra, I., Automorphic forms and Kleinian groups (1972), Benjamin: Benjamin Reading, MA · Zbl 0253.30015 [8] Kervaire, M. A.; Milnor, J., Groups of homotopy spheres I, Ann. Math., 77, 504-537 (1963) · Zbl 0115.40505 [9] Quinn, F., Ends of maps I, Ann. Math., 110, 275-331 (1979) · Zbl 0394.57022 [10] Quinn, F., Ends of maps III; Dimensions 4 and 5, J. Diff. Geom., 81, 503-521 (1982) · Zbl 0533.57009 [11] Shaneson, J. L., Wall’s surgery obstruction groups for \(Z\) × \(G\), Ann. Math., 90, 296-334 (1969) · Zbl 0182.57303 [12] Taylor, L., Noncompact surgery, UC Berkeley, Ph.D. thesis (1972) [13] Wall, C. T.C., Surgery on Compact Manifolds (1970), Academic Press: Academic Press New York · Zbl 0219.57024 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.