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A splitting theorem for manifolds. (English) Zbl 0348.57017

MSC:
57R65 Surgery and handlebodies
57M10 Covering spaces and low-dimensional topology
57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.
57R80 \(h\)- and \(s\)-cobordism
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References:
[1] BHS. Bass, H., Heller, A., Swan, R. G.: The Whitehead group of a polynomial extension. Publ. Math. I.H.E.S.22, 61-79 (1964) · Zbl 0248.18026
[2] B1. Browder, W.: Embedding 1-connected manifolds. Bull. Amer. Math. Soc.72, 225-231 (1966) · Zbl 0141.40602 · doi:10.1090/S0002-9904-1966-11477-5
[3] B2. Browder, W.: Manifolds with ?1 = Z. Bull. Amer. Math. Soc.72, 238-244 (1966) · Zbl 0136.44102 · doi:10.1090/S0002-9904-1966-11482-9
[4] B3. Browder, W.: Surgery on simply-connected manifolds. Berlin-Heidelberg-New York: Springer 1972 · Zbl 0239.57016
[5] B4. Bak, A.: Odd dimensional Wall groups of groups of odd order are zero. To appear
[6] BL. Browder, W., Levine, J.: Fibering manifolds over a circle. Comm. Math. Helv.40, 153-160 (1966) · Zbl 0134.42802 · doi:10.1007/BF02564368
[7] BLL. Browder, W., Levine, J., Livesay, G. R.: Finding a boundary for an open manifolds. Amer. J. Math.87, 1017-1028 (1965) · Zbl 0134.42801 · doi:10.2307/2373259
[8] C1. Cappell, S. E.: A splitting theorem for manifolds and surgery groups. Bull. Amer. Math. Soc.77, 281-286 (1971) · Zbl 0215.52601 · doi:10.1090/S0002-9904-1971-12720-9
[9] C2. Cappell, S. E.: Superspinning and knot complements. Topology of manifolds (Proceedings of the 1969 Georgia Conference), Markham Press, pp. 358-383, 1971
[10] C3. Cappell, S.: Mayer-Vietoris sequences in HermitianK-theory. Proc. BattelleK-theory Conf., Lecture Notes in Math.343, pp. 478-512. Berlin-Heidelberg-New York: Springer 1973
[11] C4. Cappell, S.: On homotopy invariance of higher signatures. Inventiones math33, 171-179 (1976) · Zbl 0335.57007 · doi:10.1007/BF01402341
[12] C5. Cappell, S.: Splitting obstructions for Hermitian forms and manifolds with Z2 ? ?1. Bull. Amer. Math. Soc.79, 909-914 (1973) · Zbl 0272.57016 · doi:10.1090/S0002-9904-1973-13255-0
[13] C6. Cappell, S.: On connected sums of manifolds. Topology13, 395-400 (1974) · Zbl 0291.57007 · doi:10.1016/0040-9383(74)90030-5
[14] C7. Cappell, S.: Unitary nilpotent groups and HermitianK-theory. Bull. Amer. Math. Soc.80, 1117-1122 (1974) · Zbl 0322.57020 · doi:10.1090/S0002-9904-1974-13636-0
[15] C8. Cappell, S.: Manifolds with fundamental group a generalized free product. Bull. Amer. Math. Soc.80, 1193-1198 (1974) · Zbl 0341.57007 · doi:10.1090/S0002-9904-1974-13673-6
[16] C9. Cappell, S.: Decompositions of Manifolds. To appear
[17] CS 1. Cappell, S., Shaneson, J. L.: Four-dimensional surgery and applications. Comm. Math. Helv.47, 500-528 (1972) · Zbl 0233.57015
[18] CS 2. Cappell, S., Shaneson, J. L.: The codimension two placement problem and homology equivalent manifolds. To appear in Ann. of Math. · Zbl 0279.57011
[19] CF. Conner, P. E., Floyd, E. E.: Differentiable periodic maps. Berlin-Göttingen-Heidelberg: Springer 1964 · Zbl 0125.40103
[20] F. Farrell, F. T.: The obstruction to fibering a manifold over a circle. Indiana Univ. Math. J.21, 315-346 (1971) · Zbl 0242.57016 · doi:10.1512/iumj.1971.21.21024
[21] FH1. Farrell, F. T., Hsiang, W. C.: Manifolds with ?1 G \(\times\)? T. Amer. J. Math.95, 813-848 (1973) · Zbl 0304.57009 · doi:10.2307/2373698
[22] FH2. Farrell, F. T., Hsiang, W. C.: A formula forK 1 R[T]. Proceedings of Symposia in Pure MathematicsXVII, 172-218 (1970)
[23] KM. Kervaire, M. A., Milnor, J. W.: Groups of homotopy spheres 1. Ann. of Math.77, 504-537 (1963) · Zbl 0115.40505 · doi:10.2307/1970128
[24] KS. Kirby, R. C., Siebenmann, L. C.: On the triangulation of manifolds and the Hauptvermutung. Buul. Amer. Math. Soc.75, 742-749 (1969) (see also Not. Amer Math. Soc.16, 848 (1969)) · Zbl 0189.54701 · doi:10.1090/S0002-9904-1969-12271-8
[25] KWS. Kwun, K. W., Szczarba, R.: Product and sum theorems for Whitehead torsion. Ann. of Math.82, 183-190 (1965) · Zbl 0142.40703 · doi:10.2307/1970568
[26] K 1. Kurosh, A. G.: The theory of groups. Chelsea: New York 1956
[27] K 2. Kervaire, M. A.: Le théorème de Barden-Mazur-Stallings. Comm. Math. Helv.40, 31-42 (1965) · Zbl 0135.41503 · doi:10.1007/BF02564363
[28] L 1. Lee, R.: Splitting a manifold into two parts. Mimeographed Notes, Inst. Advanced Study, 1969
[29] L 2. Lees, J.: Immersions and surgeries of topological manifolds. Bull. Amer. Math. Soc.75, 529-534 (1969) · Zbl 0176.21703 · doi:10.1090/S0002-9904-1969-12231-7
[30] M 1. Milnor, J. W.: Whitehead torsion. Bull. Amer. Math. Soc.72, 358-426 (1966) · Zbl 0147.23104 · doi:10.1090/S0002-9904-1966-11484-2
[31] M 2. Milnor, J. W.: Lectures on theh-cobordism theorem. Notes by L. Siebenmann and J. Sondow, Princeton, 1965
[32] N. Novikov, S. P.: On manifolds with free abelian fundamental group and their application (Russian). Izv. Akad. Nauk SSSR Ser. Mat.30, 207-246 (1966)
[33] R. Ranicki, A.: Algebraic L-Theory, II: Laurent Extensios Proc. London Math. Soc. XXVII. pp. 126-158 (1973) · doi:10.1112/plms/s3-27.1.126
[34] S 1. Siebenmann, L. C.: The obstruction to finding the boundary of an open manifold. Princeton Univ. Thesis 1965
[35] S 2. Shaneson, J. L.: Wall’s surgery obstruction groups forZ\(\times\)G. Ann of Math.90, 296-334 (1969) · Zbl 0182.57303 · doi:10.2307/1970726
[36] S 3. Shaneson, J. L.: Non-simply connected surgery and some results in low dimensional topology. Comm. Math. Helv.45, (1970) 333-352 (1970) · Zbl 0207.53803 · doi:10.1007/BF02567336
[37] Sp. Spanier, E. H.: Algebraic topology. New York: McGraw Hill 1966 · Zbl 0145.43303
[38] St. Stallings, J.: Whitehead torsion of free products. Ann. of Math82, pp. 354-363 (1965) · Zbl 0132.26804 · doi:10.2307/1970647
[39] St 1. Stallings, J.: On fibering certain 3-manifolds. Topology of 3-manifolds and related topics, (Proc. Georgia Conference 1961) pp. 95-100, Prentice-Hall, N.J., 1962
[40] W 1. Waldhausen, F.: Whitehead groups of generalized free products. Mimeographed preprint · Zbl 0326.18010
[41] W 2. Wall, C. T. C.: Surgery on compact manifolds. New York-London: Academic Press 1970 · Zbl 0219.57024
[42] W 3. Wall, C. T. C.: Some L groups of finite groups. Bull. Amer. Math. Soc.79, 526-529 (1973) · Zbl 0262.16027 · doi:10.1090/S0002-9904-1973-13185-4
[43] Z. Zeeman, E. C.: Unknotting combinatorial ball. Ann. of Math.78, 501-526 (1963) · Zbl 0122.17901 · doi:10.2307/1970538
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