Bibliography
V. I. Arnold,Ordinary Differential Equations, Cambridge, MIT Press, 1973.
J. F. Adams,Lectures on Lie Groups, New York, Benjamin, Inc., 1969.
M. Atiyah andR. Bott, A Lefschetz fixed point formula for elliptic complexes: II. Applications,Ann. of Math.,88 (1968), 451–491.
M. Atiyah andI. Singer, The index of elliptic operators, III,Ann. of Math.,87 (1968), 546–604.
G. Bredon, Representations at fixed points of smooth actions of compact groups,Ann. of Math.,89 (1969), 512–532.
—————,Introduction to compact transformation groups, New York, Academic Press, 1972.
C. Camacho, N. Kuiper, J. Palis, The topology of holomorphic flows with singularity,Publ. Math. I.H.E.S.,48 (1979), 5–38.
C. Curtis andI. Reiner,Representation theory of finite groups and associative algebras, New York, Interscience-Wiley, 1962.
S. E. Cappell andJ. L. Shaneson, Pseudo-free group actions I,Proc. of the Aarhus Topology Conference of 1978, Springer Lecture Notes in Math.,763 (1979), 395–447.
—————, Linear Algebra and Topology,Bull. Amer. Math. Soc., New Series,1 (1979), 685–687.
—————, Nonlinear similarity of matrices,Bull. Amer. Math. Soc., New Series,1 (1979), 899–902.
—————, Nonlinear similarity,Ann. of Math.,113 (1981), 315–355.
—————, Fixed points of periodic smooth maps,Proc. National Acad. of Sci. USA,77 (1980), 5052–5054.
----- Fixed points of periodic differentiable maps (to appear).
----- The geometry of linear representations of groups and subgroups (to appear inAmer. Jour. of Math.).
----- Matrices, topology, and elementary number theory (to appear).
----- Nonlinear similarity and linear similarity are the same in dimensions less than 6 (to appear).
----- Class numbers and periodic smooth maps (to appear).
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.
----- Reidemeister’s torsion invariant and rotation of Sn,International Conf. on Differential Analysis, Bombay Colloquium of 1964, Oxford Univ. Press, 1964, 27–36.
G. deRham, S. Maumary, andM. A. Kervaire, Torsion et type simple d’homotopie,Lecture Notes in Math.,48, Springer-Verlag, 1967.
Ju. S.Il’iašenko, Global and local aspects of the theory of complex differential equations,Proc. Int. Cong. of Math., Helsinki, 1978, 821–826.
K. Kawakubo, Weyl group actions and equivariant homotopy equivalence,Proc. of Amer. Math. Soc.,80 (1980), 172–176.
B. Klares,Classification topologique des n-tuples de champs de vecteurs holomorphes commutatifs sur P n+1(C), Thèse, Université de Strasbourg, 1980, partie II.
N. H. Kuiper, The topology of a solution of a differential equation onR n,Proc. Int. Congress on Manifolds, Tokyo, 1973, 195–203.
—————, La topologie des singularités hyperboliques des actions deR 2,Astérisque,59–60 (1978), 131–150.
----- The topology of linearC m-flows onC n, to appear in theProceedings of a Conference on Dynamical Systems, Rio de Janeiro, July 1981.
N. Kuiper andJ. W. Robbin, Topological classification of linear endomorphisms,Inventiones Math.,19 (1973), 83–106.
S. Lang,Algebra, Addison-Wesley, 1965.
C. Lee andA. Wasserman, On the groups JO(G),Memoirs Amer. Math. Soc., Vol. 2, Issue 1, No. 159, Amer. Math. Soc., Providence, R. I., 1975.
J. Milnor, Whitehead torsion,Bull. Amer. Math. Soc.,72 (1966), 358–426.
R. Oliver, Fixed point sets of group actions on finite acyclic complexes,Comment. Math. Helv.,50 (1975), 155–177.
T. Petrie, The Atiyah-Singer invariant, the Wall groups L n (, 1), and the function (te x+1)/(te x − 1),Ann. of Math.,92 (1970), 174–187.
————— G-Surgery I-A survey,Springer Lecture Notes,664 (1978), 197–233.
————— Three Theorems on Transformation Groups,Springer Lecture Notes,763 (1979), 549–572.
H. Poincaré, Sur les courbes définies par les équations différentielles,Œuvres de H. Poincaré, Vol. I, Paris, Gauthier-Villars (1926).
M. G. Rothenburg, Torsion invariants and finite transformation groups,Symposia in Pure Math., XXXII, part 1, 267–312, Amer. Math. Soc., 1978.
C. Sanchez, Actions of groups of odd order on compact, orientable manifolds,Proc. Amer. Math. Soc.,54 (1976), 445–448.
R. Schultz, On the topological classification of linear representations,Topology,16 (1977), 263–270.
J.-P. Serre,Représentations linéaires des groupes finis, Paris, Hermann (1967).
J. L. Shaneson, Wall’s surgery obstruction groups for Z × G,Ann. of Math.,90 (1969), 296–334.
P. A. Smith, New results and old problems in finite transformation groups,Bull. Amer. Math. Soc.,66 (1960), 401–415.
P. Traczyk, On the G-homotopy equivalence of spheres of representations,Math. Zeitschrift,161 (1978), 257–261.
C. T. C. Wall,Surgery on compact manifolds, New York, Academic Press, 1970.
—————, Classification of Hermitian forms, VI, group rings,Ann. of Math.,103 (1976), 1–80.
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Research supported by NSF Grant No. MCS 76-06974. The hospitality of Université de Paris at Orsay and I.H.E.S. when this work was begun is gratefully acknowledged.
Research supported by NSF Grant MCS 80-26053.
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Cappell, S.E., Shaneson, J.L. The topological rationality of linear representations. Publications Mathématiques de L’Institut des Hautes Scientifiques 56, 101–128 (1982). https://doi.org/10.1007/BF02700463
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DOI: https://doi.org/10.1007/BF02700463