Bendersky, Martin Cobordism span of a manifold and elliptic genera. (English) Zbl 0659.57017 Math. Z. 202, No. 4, 483-492 (1989). The power of two that divides the twisted signature is an obstruction to vector fields on a 4k-dimensional manifold. The universal elliptic genus is used to compute this obstruction. Reviewer: M.Bendersky Cited in 1 Document MSC: 57R25 Vector fields, frame fields in differential topology 57R20 Characteristic classes and numbers in differential topology 57R75 \(\mathrm{O}\)- and \(\mathrm{SO}\)-cobordism 58J26 Elliptic genera Keywords:twisted signature; obstruction to vector fields on a 4k-dimensional manifold; universal elliptic genus; cobordism PDFBibTeX XMLCite \textit{M. Bendersky}, Math. Z. 202, No. 4, 483--492 (1989; Zbl 0659.57017) Full Text: DOI EuDML References: [1] Atiyah, M.F.: Vector fields on manifolds. Arbeitsgemeinschaft für Forschung des Landes Nordrhein-Westfalen, Düsseldorf 969.200, 7-24 (1970) [2] Atiyah, M.F., Bott, R., Shapiro, A.: Clifford modules. Topology3 [Suppl. 1], 3-33 (1964) · Zbl 0146.19001 · doi:10.1016/0040-9383(64)90003-5 [3] Atiyah, M.F., Dupont, J.L.: Vector fields with finite singularities. Acta Math.128, 1-40 (1972) · Zbl 0233.57010 · doi:10.1007/BF02392157 [4] Frank, D.: On the index of a tangent 2-field. Topology11, 245-252 (1972) · Zbl 0252.57006 · doi:10.1016/0040-9383(72)90011-0 [5] Hirzebruch, F.: Elliptic genera of levelN for complex manifolds. (Preprint) 1988 · Zbl 0667.32009 [6] Landweber, P.S.: Elliptic cohomology and modular forms. In: Landweber, P.S. (ed.) Elliptic curves and modular forms in algebraic topology (Lect. Notes Math., vol. 1326, pp. 55-68). Berlin Heidelberg New York: Springer 1988 · Zbl 0649.57022 [7] Massey, W.: On the Stiefel-Whitney classes of a manifold, II. Proc. Am. Math. Soc.13, 938-942 (1962) · Zbl 0109.15902 · doi:10.1090/S0002-9939-1962-0142129-8 [8] Mayer, K.H.: Elliptische Differentialoperatoren und Ganzzahligkeitssätze für charakteristische Zahlen. Topology4, 295-313 (1965) · Zbl 0173.25903 · doi:10.1016/0040-9383(65)90013-3 [9] Ochanine, S.: Sur les genres multiplicatifs définis par des intégrales elliptiques. Topology26, 143-151 (1987) · Zbl 0626.57014 · doi:10.1016/0040-9383(87)90055-3 [10] Ochanine, S.: Signature modulo 16, invariants de Kervaire généralisés, et nombres caractéristiques dans laK-théorie réelle: Supplément au Bull. Soc. Math. Fr.109, Mémoire no. 5 (1981) [11] Palais, R.: Seminar on the Atiyah-Singer Index Theorem. Ann. Math. Stud. no. 57 (1965) · Zbl 0137.17002 [12] Reed, J.: Killing cohomology classes by surgery. Proceedings of the advanced study institute of algebraic topology, vol. II. (Aarhus Universitet various publications series no. 13, pp. 446-454) 1970 [13] Tamanoi, H.: (Hyper)elliptic genera. Thesis. Johns Hopkins University. (1987) [14] Tamanoi, H.: I finite dimensional symmetry on Elliptic genera (to appear) · Zbl 1052.17015 [15] Thomas, P.E.: The index of a tangent 2-field. Comment. Math. Phys.42, 86-110 (1967) · Zbl 0153.53504 · doi:10.1007/BF02564413 [16] Witten, E.: Elliptic genera and quantum field theory. Commun. Matth. Phys.109, 525-536 (1987) · Zbl 0625.57008 · doi:10.1007/BF01208956 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.