The topological rationality of linear representations
Publications Mathématiques de l'IHÉS, Tome 56 (1982), pp. 101-128.
@article{PMIHES_1982__56__101_0,
     author = {Cappell, Sylvain E. and Shaneson, Julius L.},
     title = {The topological rationality of linear representations},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {101--128},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {56},
     year = {1982},
     mrnumber = {686043},
     zbl = {0507.57028},
     language = {en},
     url = {http://archive.numdam.org/item/PMIHES_1982__56__101_0/}
}
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Cappell, Sylvain E.; Shaneson, Julius L. The topological rationality of linear representations. Publications Mathématiques de l'IHÉS, Tome 56 (1982), pp. 101-128. http://archive.numdam.org/item/PMIHES_1982__56__101_0/

[A] V. I. Arnold, Ordinary Differential Equations, Cambridge, MIT Press, 1973. | MR | Zbl

[Ad] J. F. Adams, Lectures on Lie Groups, New York, Benjamin, Inc., 1969. | MR | Zbl

[AB] M. Atiyah and R. Bott, A Lefschetz fixed point formula for elliptic complexes : II. Applications, Ann. of Math., 88 (1968), 451-491. | MR | Zbl

[AS] M. Atiyah and I. Singer, The index of elliptic operators, III, Ann. of Math., 87 (1968), 546-604. | MR | Zbl

[Bre 1] G. Bredon, Representations at fixed points of smooth actions of compact groups, Ann. of Math., 89 (1969), 512-532. | MR | Zbl

[Bre 2] G. Bredon, Introduction to compact transformation groups, New York, Academic Press, 1972. | MR | Zbl

[CKP] C. Camacho, N. Kuiper, J. Palis, The topology of holomorphic flows with singularity, Publ. Math. I.H.E.S., 48 (1979), 5-38. | Numdam | MR | Zbl

[CR] C. Curtis and I. Reiner, Representation theory of finite groups and associative algebras, New York, Interscience-Wiley, 1962. | MR | Zbl

[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. | MR | Zbl

[CS 2] S. E. Cappell and J. L. Shaneson, Linear Algebra and Topology, Bull. Amer. Math. Soc., New Series, 1 (1979), 685-687. | MR | Zbl

[CS 3] S. E. Cappell and J. L. Shaneson, Nonlinear similarity of matrices, Bull. Amer. Math. Soc., New Series, 1 (1979), 899-902. | MR | Zbl

[CS 4] S. E. Cappell and J. L. Shaneson, Nonlinear similarity, Ann. of Math., 113 (1981), 315-355. | MR | Zbl

[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. | MR | Zbl

[CS 6] S. E. Cappell and J. L. Shaneson, Fixed points of periodic differentiable maps (to appear). | Zbl

[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.).

[CS 8] S. E. Cappell and J. L. Shaneson, Matrices, topology, and elementary number theory (to appear).

[CS 9] S. E. Cappell and J. L. Shaneson, Nonlinear similarity and linear similarity are the same in dimensions less than 6 (to appear). | Zbl

[CS 10] S. E. Cappell and J. L. Shaneson, Class numbers and periodic smooth maps (to appear). | Zbl

[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. | JFM | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | Zbl

[Ka] K. Kawakubo, Weyl group actions and equivariant homotopy equivalence, Proc. of Amer. Math. Soc., 80 (1980), 172-176. | MR | Zbl

[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.

[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. | Zbl

[K 2] N. H. Kuiper, La topologie des singularités hyperboliques des actions de R2, Astérisque, 59-60 (1978), 131-150. | Numdam | MR | Zbl

[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.

[KR] N. Kuiper and J. W. Robbin, Topological classification of linear endomorphisms, Inventiones Math., 19 (1973), 83-106. | MR | Zbl

[L] S. Lang, Algebra, Addison-Wesley, 1965. | MR | Zbl

[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. | MR | Zbl

[M] J. Milnor, Whitehead torsion, Bull. Amer. Math. Soc., 72 (1966), 358-426. | MR | Zbl

[O] R. Oliver, Fixed point sets of group actions on finite acyclic complexes, Comment. Math. Helv., 50 (1975), 155-177. | MR | Zbl

[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. | MR | Zbl

[Pe 2] T. Petrie, G-Surgery I-A survey, Springer Lecture Notes, 664 (1978), 197-233. | MR | Zbl

[Pe 3] T. Petrie, Three Theorems on Transformation Groups, Springer Lecture Notes, 763 (1979), 549-572. | MR | Zbl

[P] H. Poincaré, Sur les courbes définies par les équations différentielles, OEuvres de H. Poincaré, Vol. I, Paris, Gauthier-Villars (1926).

[R] M. G. Rothenburg, Torsion invariants and finite transformation groups, Symposia in Pure Math., XXXII, part I, 267-312, Amer. Math. Soc., 1978. | MR | Zbl

[Sa] C. Sanchez, Actions of groups of odd order on compact, orientable manifolds, Proc. Amer. Math. Soc., 54 (1976), 445-448. | MR | Zbl

[Sch] R. Schultz, On the topological classification of linear representations, Topology, 16 (1977), 263-270. | MR | Zbl

[Se] J.-P. Serre, Représentations linéaires des groupes finis, Paris, Hermann (1967). | MR | Zbl

[Sh] J. L. Shaneson, Wall's surgery obstruction groups for Z X G, Ann. of Math., 90 (1969), 296-334. | MR | Zbl

[Sm] P. A. Smith, New results and old problems in finite transformation groups, Bull. Amer. Math. Soc., 66 (1960), 401-415. | MR | Zbl

[Tr] P. Traczyk, On the G-homotopy equivalence of spheres of representations, Math. Zeitschrift, 161 (1978), 257-261. | MR | Zbl

[W 1] C. T. C. Wall, Surgery on compact manifolds, New York, Academic Press, 1970. | MR | Zbl

[W 2] C. T. C. Wall, Classification of Hermitian forms, VI, group rings, Ann. of Math., 103 (1976), 1-80. | MR | Zbl