The topological rationality of linear representations

 Access to full text

 Full (PDF)

1. [A] V. I. ARNOLD, Ordinary Differential Equations, Cambridge, MIT Press, 1973. Zbl0296.34001MR50 #13679
2. [Ad] J. F. ADAMS, Lectures on Lie Groups, New York, Benjamin, Inc., 1969. Zbl0206.31604MR40 #5780
3. [AB] M. ATIYAH and R. BOTT, A Lefschetz fixed point formula for elliptic complexes : II. Applications, Ann. of Math., 88 (1968), 451-491. Zbl0167.21703MR38 #731
4. [AS] M. ATIYAH and I. SINGER, The index of elliptic operators, III, Ann. of Math., 87 (1968), 546-604. Zbl0164.24301MR38 #5245
5. [Bre 1] G. BREDON, Representations at fixed points of smooth actions of compact groups, Ann. of Math., 89 (1969), 512-532. Zbl0162.27404MR39 #7628
6. [Bre 2] G. BREDON, Introduction to compact transformation groups, New York, Academic Press, 1972. Zbl0246.57017MR54 #1265
7. [CKP] C. CAMACHO, N. KUIPER, J. PALIS, The topology of holomorphic flows with singularity, Publ. Math. I.H.E.S., 48 (1979), 5-38. Zbl0411.58018MR80j:58045
8. [CR] C. CURTIS and I. REINER, Representation theory of finite groups and associative algebras, New York, Interscience-Wiley, 1962. Zbl0131.25601MR26 #2519
9. [CS 1] S. E. CAPPELL and J. L. SHANESON, Pseudo-free group actions I, Proc. of the Aarhus Topology Conference of 1978, Springer Lecture Notes in Math., 763 (1979), 395-447. Zbl0416.57020MR81d:57034
10. [CS 2] S. E. CAPPELL and J. L. SHANESON, Linear Algebra and Topology, Bull. Amer. Math. Soc., New Series, 1 (1979), 685-687. Zbl0412.57030MR80f:57016
11. [CS 3] S. E. CAPPELL and J. L. SHANESON, Nonlinear similarity of matrices, Bull. Amer. Math. Soc., New Series, 1 (1979), 899-902. Zbl0449.57012MR80m:57010
12. [CS 4] S. E. CAPPELL and J. L. SHANESON, Nonlinear similarity, Ann. of Math., 113 (1981), 315-355. Zbl0477.57022MR83h:57060
13. [CS 5] S. E. CAPPELL and J. L. SHANESON, Fixed points of periodic smooth maps, Proc. National Acad. of Sci. USA, 77 (1980), 5052-5054. Zbl0448.57018MR81m:57029
14. [CS 6] S. E. CAPPELL and J. L. SHANESON, Fixed points of periodic differentiable maps (to appear). Zbl0507.57027
15. [CS 7] S. E. CAPPELL and J. L. SHANESON, The geometry of linear representations of groups and subgroups (to appear in Amer. Jour. of Math.). Zbl0935.15011
16. [CS 8] S. E. CAPPELL and J. L. SHANESON, Matrices, topology, and elementary number theory (to appear). 
17. [CS 9] S. E. CAPPELL and J. L. SHANESON, Nonlinear similarity and linear similarity are the same in dimensions less than 6 (to appear). Zbl0935.15011
18. [CS 10] S. E. CAPPELL and J. L. SHANESON, Class numbers and periodic smooth maps (to appear). Zbl0528.57032
19. [DeR 1] G. de RHAM, Sur les nouveaux invariants topologiques de M. Reidemeister, International Conference of Topology (Moscow, 1935), Recueil Mathématique, Moscow, 1936, t. I (43), 737-743. Zbl0016.04501JFM62.0662.04
20. [DeR 2] G. de RHAM, Reidemeister's torsion invariant and rotation of Sn, International Conf. on Differential Analysis, Bombay Colloquium of 1964, Oxford Univ. Press, 1964, 27-36. Zbl0145.44004MR32 #8355
21. [DeR 3] G. de RHAM, S. MAUMARY, and M. A. KERVAIRE, Torsion et type simple d'homotopie, Lecture Notes in Math., 48, Springer-Verlag, 1967. Zbl0153.53901MR36 #5943
22. [I] Ju. S. IL'IAŠENKO, Global and local aspects of the theory of complex differential equations, Proc. Int. Cong. of Math., Helsinki, 1978, 821-826. Zbl0434.34003
23. [Ka] K. KAWAKUBO, Weyl group actions and equivariant homotopy equivalence, Proc. of Amer. Math. Soc., 80 (1980), 172-176. Zbl0443.57024MR81j:57022
24. [Kla] B. KLARES, Classification topologique des n-tuples de champs de vecteurs holomorphes commutatifs sur Pn+1(C), Thèse, Université de Strasbourg, 1980, partie II. 
25. [K 1] N. H. KUIPER, The topology of a solution of a differential equation on Rn, Proc. Int. Congress on Manifolds, Tokyo, 1973, 195-203. Zbl0308.34036
26. [K 2] N. H. KUIPER, La topologie des singularités hyperboliques des actions de R2, Astérisque, 59-60 (1978), 131-150. Zbl0476.58015MR81g:58028
27. [K 3] N. H. KUIPER, The topology of linear Cm-flows on Cn, to appear in the Proceedings of a Conference on Dynamical Systems, Rio de Janeiro, July 1981. 
28. [KR] N. KUIPER and J. W. ROBBIN, Topological classification of linear endomorphisms, Inventiones Math., 19 (1973), 83-106. Zbl0251.58008MR47 #8567
29. [L] S. LANG, Algebra, Addison-Wesley, 1965. Zbl0193.34701MR33 #5416
30. [LW] C. LEE and A. WASSERMAN, On the groups JO(G), Memoirs Amer. Math. Soc., Vol. 2, Issue I, No. 159, Amer. Math. Soc., Providence, R. I., 1975. Zbl0323.55031MR51 #6808
31. [M] J. MILNOR, Whitehead torsion, Bull. Amer. Math. Soc., 72 (1966), 358-426. Zbl0147.23104MR33 #4922
32. [O] R. OLIVER, Fixed point sets of group actions on finite acyclic complexes, Comment. Math. Helv., 50 (1975), 155-177. Zbl0304.57020MR51 #11556
33. [Pe 1] T. PETRIE, The Atiyah-Singer invariant, the Wall groups Ln( , 1), and the function (tex + 1)/(tex - 1), Ann. of Math., 92 (1970), 174-187. Zbl0205.53802MR47 #7761
34. [Pe 2] T. PETRIE, G-Surgery I-A survey, Springer Lecture Notes, 664 (1978), 197-233. Zbl0403.57003MR80g:57049
35. [Pe 3] T. PETRIE, Three Theorems on Transformation Groups, Springer Lecture Notes, 763 (1979), 549-572. Zbl0419.57011MR82b:57031
36. [P] H. POINCARÉ, Sur les courbes définies par les équations différentielles, OEuvres de H. Poincaré, Vol. I, Paris, Gauthier-Villars (1926). Zbl18.0314.01
37. [R] M. G. ROTHENBURG, Torsion invariants and finite transformation groups, Symposia in Pure Math., XXXII, part I, 267-312, Amer. Math. Soc., 1978. Zbl0426.57013MR80j:57038
38. [Sa] C. SANCHEZ, Actions of groups of odd order on compact, orientable manifolds, Proc. Amer. Math. Soc., 54 (1976), 445-448. Zbl0316.57022MR53 #11641
39. [Sch] R. SCHULTZ, On the topological classification of linear representations, Topology, 16 (1977), 263-270. Zbl0367.55018MR58 #18449
40. [Se] J.-P. SERRE, Représentations linéaires des groupes finis, Paris, Hermann (1967). Zbl0189.02603MR38 #1190
41. [Sh] J. L. SHANESON, Wall's surgery obstruction groups for Z X G, Ann. of Math., 90 (1969), 296-334. Zbl0182.57303MR39 #7614
42. [Sm] P. A. SMITH, New results and old problems in finite transformation groups, Bull. Amer. Math. Soc., 66 (1960), 401-415. Zbl0096.37501MR23 #A2880
43. [Tr] P. TRACZYK, On the G-homotopy equivalence of spheres of representations, Math. Zeitschrift, 161 (1978), 257-261. Zbl0365.22014MR58 #13025
44. [W 1] C. T. C. WALL, Surgery on compact manifolds, New York, Academic Press, 1970. Zbl0219.57024MR55 #4217
45. [W 2] C. T. C. WALL, Classification of Hermitian forms, VI, group rings, Ann. of Math., 103 (1976), 1-80. Zbl0328.18006MR55 #5720