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Splitting obstructions for Hermitian forms and manifolds with \(Z_2 \subset \pi_1\). (English) Zbl 0272.57016

MSC:
57N35 Embeddings and immersions in topological manifolds
57Q35 Embeddings and immersions in PL-topology
57R40 Embeddings in differential topology
57R65 Surgery and handlebodies
16E20 Grothendieck groups, \(K\)-theory, etc.
18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects)
55P10 Homotopy equivalences in algebraic topology
20H25 Other matrix groups over rings
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References:
[1] William Browder, Manifolds with \?\(_{1}\)=\?, Bull. Amer. Math. Soc. 72 (1966), 238 – 244. · Zbl 0136.44102
[2] Sylvain Cappell, A splitting theorem for manifolds and surgery groups, Bull. Amer. Math. Soc. 77 (1971), 281 – 286. · Zbl 0215.52601
[3] Sylvain E. Cappell, Mayer-Vietoris sequences in hermitian \?-theory, Algebraic K-theory, III: Hermitian K-theory and geometric applications (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972) Springer, Berlin, 1973, pp. 478 – 512. Lecture Notes in Math., Vol. 343.
[4] Sylvain E. Cappell, A splitting theorem for manifolds, Invent. Math. 33 (1976), no. 2, 69 – 170. · Zbl 0348.57017 · doi:10.1007/BF01402340 · doi.org
[5] S. E. Cappell, The unitary nilpotent category and Hermitian K-theory (to appear).
[6] R. Lee, Splitting a manifold into two parts, Inst. Advanced Study Mimeographed Notes, Princeton, N. J., 1969.
[7] A. S. Miščenko, Homotopy invariants of multiply connected manifolds. II. Simple homotopy type, Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971), 655 – 666 (Russian).
[8] C. T. C. Wall, Surgery on compact manifolds, Academic Press, London-New York, 1970. London Mathematical Society Monographs, No. 1. · Zbl 0219.57024
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