Higher $G$-indices and applications

 Access to full text

 Full (PDF)

1. [1] A. H. ASSADI and P. VOGEL, Semifree Finite Group Actions on Compact Manifolds, in Algebraic and Geometric Topology (Proceedings, Rutgers 1983), A. RANICKI, N. LEVITT and F. QUINN Eds., Lecture Notes in Math., No. 1126, Springer, Berlin and New York, 1985, pp. 1-21. Zbl0566.57023MR87d:57028
2. [2] M. F. ATIYAH and F. HIRZEBRUCH, Spin-Manifolds and Group Actions, in Essays on Topology and Related Topics : Mémoires dédiées à Georges de Rham, A. HAEFLIGER and R. NARASIMHAN Eds., Springer, New York and Heidelberg, 1970, pp. 18-28. Zbl0193.52401MR43 #4064
3. [3] M. F. ATIYAH and G. B. SEGAL, Equivariant K-Theory and Completion (J. Differential Geometry, Vol. 3, 1969, pp. 1-18). Zbl0215.24403MR41 #4575
4. [4] M. F. ATIYAH and I. M. SINGER, The Index of Elliptic Operators, III (Ann. of Math., Vol. 87, 1968, pp. 546-604). Zbl0164.24301MR38 #5245
5. [5] L. BÉRARD BERGERY, Scalar Curvature and Isometry Group in Proc. Franco-Japanese Seminar on Riemannian Geometry, Kyoto, 1981 (to appear). 
6. [6] G. E. BREDON, Introduction to Compact Transformation Groups, Academic Press, New York, 1972. Zbl0246.57017MR54 #1265
7. [7] W. BROWDER and W.-C. HSIANG, G-Actions and the Fundamental Group (Invent. Math., Vol. 65, 1982, pp. 411-424). Zbl0519.57034MR83d:57026
8. [8] S. CAPPELL, On Homotopy Invariance of Higher Signatures (Invent. Math., Vol. 33, 1976, pp. 171-179). Zbl0335.57007MR55 #11264
9. [9] P. E. CONNER, Differentiable Periodic Maps, 2nd ed., Lecture Notes in Math., No. 738, Springer, New York and Heidelberg, 1979. Zbl0417.57019MR81f:57018
10. [10] T. FACK, K-théorie bivariante de Kasparov [Séminaire Bourbaki, 1982-1983, exposé No. 605 (Astérisque, No. 105-106, 1983, pp. 149-166)]. Zbl0542.46039MR86f:46075
11. [11] T. FACK, Sur la conjecture de Novikov, in Index Theory of Elliptic Operators, Foliations, and Operator Algebras, J. KAMINKER, K. MILLETT, and C. SCHOCHET Eds., Contemp. Math., Vol. 70, Amer. Math. Soc., Providence, 1988, pp. 43-102. Zbl0658.57013MR90e:58150
12. [12] M. HILSUM, The Signature Operator of Lipschitz Manifolds and Unbounded Kasparov Bimodules, in Operator Algebras and their Connections with Topology and Ergodic Theory [Proc. Conf. at Busteni, Romania, 1983, H. ARAKI et al., Eds. (Lecture Notes in Math., No. 1132, Springer, Berlin and New York, 1985, pp. 254-288)]. Zbl0602.46069MR87d:58133
13. [13] J. KAMINKER and J. C. MILLER, Homotopy Invariance of the Analytic Index of Signature Operators Over C*-Algebras (J. Operator Theory, Vol. 14, 1985, pp. 113-127). Zbl0614.46062MR87b:58082
14. [14] G. G. KASPAROV, The Operator K-Functor and Extensions of C*-Algebras (Izv. Akad. Nauk S.S.S.R., Ser. Mat., Vol. 44, 1980, pp. 571-636 = Math. U.S.S.R.-Izv., 16, 1981, pp. 513-572). Zbl0464.46054MR81m:58075
15. [15] G. G. KASPAROV, Operator K-Theory and its Applications : Elliptic Operators, Group Representations, Higher Signatures, C*-Extensions, in Proc. International Congress of Mathematicians, Warsaw, 1983, Polish Scientific Publishers, Warsaw, Vol. 2, 1984, pp. 987-1000. Zbl0571.46047MR87c:58119
16. [16] G. G. KASPAROV, Equivariant KK-Theory and the Novikov Conjecture (Invent. Math., Vol. 91, 1988, pp. 147-201). Zbl0647.46053MR88j:58123
17. [17] P. S. LANDWEBER and R. E. STONG, Circle Actions on Spin Manifolds and Characteristic Numbers, (Topology, Vol. 27, 1988, pp. 145-161). Zbl0647.57013MR90a:57040
18. [18] H. B. LAWSON Jr., and S.-T. YAU, Scalar Curvature, Non-Abelian Group Actions and the Degree of Symmetry of Exotic Spheres (Comm. Math. Helv., Vol. 49, 1974, pp. 232-244). Zbl0297.57016MR50 #11300
19. [19] A. S. MIŠČENKO, Homotopy Invariants of Nonsimply Connected Manifolds, I : Rational Invariants (Izv. Akad. Nauk S.S.S.R., Ser. Mat., Vol. 34, 1970, pp. 501-514 = Math. U.S.S.R.-Izv., Vol. 4, 1970, pp. 506-519). Zbl0232.55015
20. [20] A. S. MIŠČENKO, Hermitian K-Theory : the Theory of Characteristic Classes and Methods of Functional Analysis (Usp. Mat. Nauk., Vol. 31, 1976, No. 2, pp. 69-134 = Russian Math. Surveys, Vol. 31, No. 2, 1976, pp. 71-138). Zbl0427.55001
21. [21] A. S. MIŠČENKO and A. T. FOMENKO, The Index of Elliptic Operators Over C*-Algebras (Izv. Akad. Nauk S.S.S.R., Ser. Mat., Vol. 43, 1979, pp. 831-859 = Math. U.S.S.R.-Izv., Vol. 15, 1980, pp. 87-112). Zbl0448.46039
22. [22] A. RANICKI, Exact Sequences in the Algebraic Theory of Surgery (Mathematical Notes, No. 26, Princeton Univ. Press, Princeton, 1981). Zbl0471.57012MR82h:57027
23. [23] J. ROSENBERG, C*-Algebras, Positive Scalar Curvature, and the Novikov Conjecture (Publ. Math. I.H.E.S., No. 58, 1983, pp. 197-212). Zbl0526.53044MR85g:58083
24. [24] J. ROSENBERG, Ibid., II, in Proc. U.S.-Japan Seminar on Geometric Methods in Operator Algebras, Kyoto, 1983, H. ARAKI and E. G. EFFROS Eds. (Pitman Res. Notes in Math., No. 123, Longman/Wiley, Harlow and New York, 1986, pp. 341-374). Zbl0658.53039
25. [25] J. ROSENBERG, Ibid., III (Topology, Vol. 25, 1986, pp. 319-336). Zbl0605.53020MR88f:58141
26. [26] J. A. SCHAFER, A Relation Between Group Actions and Index, in Proc. Conf. on Transformation Groups, New Orleans, LA, 1967, Springer, New York, 1968, pp. 349-350. Zbl0182.57502MR41 #4578
27. [27] G. B. SEGAL, Equivariant K-Theory (Publ. Math. I.H.E.S., No. 34, 1968, pp. 129-151). Zbl0199.26202MR38 #2769
28. [28] N. TELEMAN, The Index of the Signature Operator on Lipschitz Manifolds (Publ. Math. I.H.E.S., No. 58, 1983, pp. 39-78). Zbl0531.58044MR85f:58112
29. [29] N. TELEMAN, The Index Theorem for Topological Manifolds (Acta Math., Vol. 153, 1984, pp. 117-152). Zbl0547.58036MR86c:58137
30. [30] C. T. C. WALL, On Simply-Connected 4-Manifolds (J. London Math. Soc., Vol. 39, 1964, pp. 141-149). Zbl0131.20701MR29 #627
31. [31] S. WEINBERGER, Group Actions and Higher Signatures (Proc. Nat. Acad. Sci. U.S.A., Vol. 82, 1985, pp. 1297-1298). Zbl0569.57027MR88g:57044
32. [32] S. WEINBERGER, Group Actions and Higher Signatures, II (Comm. Pure Appl. Math., Vol. 40, 1987, pp. 179-187). Zbl0647.57012MR88k:57042