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K-theory obstructions to the existence of vector fields. (English) Zbl 0313.57012

MSC:
57R25 Vector fields, frame fields in differential topology
55U15 Chain complexes in algebraic topology
55S25 \(K\)-theory operations and generalized cohomology operations in algebraic topology
57R20 Characteristic classes and numbers in differential topology
55S35 Obstruction theory in algebraic topology
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[1] Adams, J. F., Vector fields on spheres.Ann. of Math., 75 (1962), 603–632. · Zbl 0112.38102
[2] Atiyah, M. F., Bott periodicity and the index of elliptic operators.Quart. J. Math. Oxford Ser., 19 (1968), 113–140. · Zbl 0159.53501
[3] –,K-theory and reality.Quart. J. Math. Oxford Ser., 17 (1966), 367–386. · Zbl 0146.19101
[4] –, Power operations inK-theory.Quart. J. Math. Oxford Ser., 17 (1966), 165–193. · Zbl 0144.44901
[5] Atiyah, M. F.,Vector fields on manifolds, Arbeitsgemeinschaft für Forschung des Landes Nordrhein-Westfalen, Heft 200.
[6] Atiyah, M. F., Bott, R. &Shapiro, A., Clifford modules.Topology, 3 (1964), Supplement 1, 3–33. · Zbl 0146.19001
[7] Atiyah, M. F. &Dupont, J. L., Vector fields with finite singularities.Acta Math., 128 (1972), 1–40. · Zbl 0233.57010
[8] Atiyah, M. F. &Singer, I. M., The index of elliptic operators I.Ann. of Math., 87 (1968), 484–530. · Zbl 0164.24001
[9] –, The index of elliptic operators III,Ann. of Math., 87 (1968), 546–603. · Zbl 0164.24301
[10] –, The index of elliptic operators IV,Ann. of Math., 93 (1971), 139–149. · Zbl 0212.28603
[11] Dold, A.,Halbexakte Homotopiefunktoren. Lecture Notes in Mathematics 12, Springer-Verlag, Berlin, Heidelberg, New York, 1966.
[12] Dupont, J. L. &Lusztig, G., On manifolds satisfyingw 1 2 =0.Topology, 10 (1971), 81–92. · Zbl 0212.28801
[13] Hirzebruch, F.,Topological methods in algebraic geometry. Grundlehren Math. Wissensch. 131, 3rd edition, Springer-Verlag, Berlin, Heidelberg, New York, 1966. · Zbl 0138.42001
[14] Massey, W., On the Stiefel-Whitney classes of a manifold II.Proc. Amer. Math. Soc., 13 (1962), 938–942. · Zbl 0109.15902
[15] Mayer, K. H., Elliptische Differentialoperatoren und Ganzzahligkeitssätze für charakteristische Zahlen.Topology, 4 (1965), 295–313. · Zbl 0173.25903
[16] Steenrod, N.,Topology of fibre bundles. Princeton Mathematical Series, Princeton University Press, Princeton N.J. 1951. · Zbl 0054.07103
[17] Thomas, E., The span of a manifold.Quart. J. Math. Oxford Ser., 19 (1968), 225–244. · Zbl 0167.51901
[18] –, Vector fields on manifolds.Bull. Amer. Math. Soc., 75 (1969), 643–683. · Zbl 0183.51703
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