Petrie, Ted Smooth S\(^1\) actions on homotopy complex projective spaces and related topics. (English) Zbl 0247.57010 Bull. Am. Math. Soc. 78, 105-153 (1972). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 9 ReviewsCited in 36 Documents MSC: 57R60 Homotopy spheres, Poincaré conjecture 57S15 Compact Lie groups of differentiable transformations PDFBibTeX XMLCite \textit{T. Petrie}, Bull. Am. Math. Soc. 78, 105--153 (1972; Zbl 0247.57010) Full Text: DOI References: [1] M. F. Atiyah, On the \?-theory of compact Lie groups, Topology 4 (1965), 95 – 99. · Zbl 0136.21001 [2] M. F. Atiyah, \?-theory, Lecture notes by D. W. Anderson, W. A. Benjamin, Inc., New York-Amsterdam, 1967. [3] 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). · Zbl 0193.52303 [4] M. F. Atiyah, R. Bott, and A. Shapiro, Clifford modules, Topology 3 (1964), no. suppl. 1, 3 – 38. · Zbl 0146.19001 [5] Michael Atiyah and Friedrich Hirzebruch, Spin-manifolds and group actions, Essays on Topology and Related Topics (Mémoires dédiés à Georges de Rham), Springer, New York, 1970, pp. 18 – 28. · Zbl 0193.52401 [6] M. F. Atiyah and G. B. Segal, The index of elliptic operators. II, Ann. of Math. (2) 87 (1968), 531 – 545. · Zbl 0164.24201 [7] M. F. Atiyah and I. M. Singer, The index of elliptic operators. I, Ann. of Math. (2) 87 (1968), 484 – 530. · Zbl 0164.24001 [8] Hyman Bass, Algebraic \?-theory, W. A. Benjamin, Inc., New York-Amsterdam, 1968. · Zbl 0174.30302 [9] Raoul Bott, The index theorem for homogeneous differential operators, Differential and Combinatorial Topology (A Symposium in Honor of Marston Morse), Princeton Univ. Press, Princeton, N.J., 1965, pp. 167 – 186. · Zbl 0173.26001 [10] Glen E. Bredon, The cohomology ring structure of a fixed point set, Ann. of Math. (2) 80 (1964), 524 – 537. · Zbl 0125.40004 [11] L. Hodgkin, An equivariant Künneth formula in K-theory, Notes, University of Warwick. · Zbl 0323.55009 [12] W. Y. Hsiang, On generalizations of a theorem of A. Borel and their applications in the study of topological actions, Topology of Manifolds, Markham, Chicago, Ill., 1970, pp.274-290. [13] C. N. Lee, Equivariant homology theories, Proc. Conf. on Transformation Groups (New Orleans, La., 1967) Springer, New York, 1968, pp. 237 – 244. [14] J. Milnor, The representation rings of some classical groups, Notes, Princeton University, Princeton, N.J., 1963. [15] John W. Milnor, Infinite cyclic coverings, Conference on the Topology of Manifolds (Michigan State Univ., E. Lansing, Mich., 1967) Prindle, Weber & Schmidt, Boston, Mass., 1968, pp. 115 – 133. [16] T. E. Stewart, Lifting the action of a group in a fibre bundle, Bull. Amer. Math. Soc. 66 (1960), 129 – 132. · Zbl 0128.16804 [17] J. C. Su, Transformation groups on cohomology projective spaces, Trans. Amer. Math. Soc. 106 (1963), 305 – 318. · Zbl 0109.41501 [18] D. Sullivan, Geometric topology seminar, Notes, Princeton University, Princeton, N.J., 1967. [19] A. Vasquez, Poincaré duality for K (to appear). [20] Deane Montgomery and C. T. Yang, Differentiable actions on homotopy seven spheres. II, Proc. Conf. on Transformation Groups (New Orleans, La., 1967) Springer, New York, 1968, pp. 125 – 134. 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.