Tangent $2$-fields on even-dimensional nonorientable manifolds
HTML articles powered by AMS MathViewer
- by Benedict J. Pollina PDF
- Trans. Amer. Math. Soc. 271 (1982), 215-224 Request permission
Abstract:
This paper uses the Postnikov decomposition of a nonsimple fibration to describe the obstructions to a tangent $2$-field on an even-dimensional nonorientable manifold.References
- Michael F. Atiyah, Vector fields on manifolds, Arbeitsgemeinschaft für Forschung des Landes Nordrhein-Westfalen, Heft 200, Westdeutscher Verlag, Cologne, 1970 (English, with German and French summaries). MR 0263102
- M. F. Atiyah and J. L. Dupont, Vector fields with finite singularities, Acta Math. 128 (1972), 1–40. MR 451256, DOI 10.1007/BF02392157
- David Frank, On the index of a tangent $2$-field, Topology 11 (1972), 245–252. MR 298689, DOI 10.1016/0040-9383(72)90011-0
- J. F. McClendon, Higher order twisted cohomology operations, Invent. Math. 7 (1969), 183–214. MR 250302, DOI 10.1007/BF01404305
- James F. McClendon, Obstruction theory in fiber spaces, Math. Z. 120 (1971), 1–17. MR 296943, DOI 10.1007/BF01109713
- C. A. Robinson, Moore-Postnikov systems for non-simple fibrations, Illinois J. Math. 16 (1972), 234–242. MR 298664
- Jerrold Siegel, Higher order cohomology operations in local coefficient theory, Amer. J. Math. 89 (1967), 909–931. MR 225319, DOI 10.2307/2373410
- Norman Steenrod, The Topology of Fibre Bundles, Princeton Mathematical Series, vol. 14, Princeton University Press, Princeton, N. J., 1951. MR 0039258
- Emery Thomas, Seminar on fiber spaces, Lecture Notes in Mathematics, vol. 13, Springer-Verlag, Berlin-New York, 1966. Lectures delivered in 1964 in Berkeley and 1965 in Zürich; Berkeley notes by J. F. McClendon. MR 0203733
- Emery Thomas, Vector fields on manifolds, Bull. Amer. Math. Soc. 75 (1969), 643–683. MR 242189, DOI 10.1090/S0002-9904-1969-12240-8 W. J. Wu, Classes-caracteristique et $i$-carrés d’une varieté, C. R. Acad. Sci. Paris 230 (1950), 508-511.
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 271 (1982), 215-224
- MSC: Primary 57R25; Secondary 55S45
- DOI: https://doi.org/10.1090/S0002-9947-1982-0648087-9
- MathSciNet review: 648087