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References
M. Atiyah and F. Hirzebruch, Riemann-Roch theorems for differentiable manifolds, Bull. Amer. Math. Soc 65 (1959), 276–281.
A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces. II, Amer. J. Math. 81 (1959), 315–382.
Z. I. Borevich and I. R. Shafarevich, Number Theory (Transl. from Russian by N. Greenleaf), Pure and Applied Mathematics Vol. 20. Academic Press, New York, 1966.
W. Browder, On the action of Θn (∂π), Differential and Combinatorial Topology (A Symposium in Honor of M. Morse), Princeton Mathematical Senes No. 27, 23–56. Princeton University Press, Princeton, 1965.
_____, Diffeomorphisms of 1-connected manifolds, Trans. Amer. Math. Soc. 128 (1967), 155–163.
G. Brumfiel, On the homotopy groups of BPL and PL/O, Ann. of Math. 88 (1968) 291–311.
_____, Homotopy equivalences of almost closed manifolds, Comment. Math. Helv. 46 (1971), 381–407; ibid., Proc. Sympos. Pure Math. 22, 73–79. American Mathematical Society, Providence, 1971.
_____, [Free] differentiable S1 actions on homotopy spheres, preprint, University of California-Berkeley, 1968.
J. Cerf, La stratification naturelle des espaces de fonctions différentiables réeles et la théorème de la pseudo-isotopie, Inst. Hautes Études Sci. Pub. Math. 39 (1970), 5–173.
P. Conner and F. Raymond, Manifolds with few periodic homeomorphisms, Proc. Second Conference on Compact Transformation Groups (Univ. of Mass., Amherst, 1971) Lecture Notes in Mathematics Vol. 299, 1–75 Springer, New York, 1972.
J. Ewing, Spheres as fixed point sets, Quart. J. Math. Oxford (2) 27, (1976) 445–455.
_____, Semifree actions of finite groups on homotopy spheres, preprint, Indiana University and University of Virginia, 1977.
W. Fenchel, Bemaerkninger om endlige grupper af afbildnings-klasser, Mat. Tidsskr. B, Årg. 1950, 90–95.
A. Hatcher, The second obstruction for pseudo-isotopies, Astérisque 6, 239–275. Société Mathématique de France, Paris, 1973.
W. Heil and J. L. Tollefson, Deforming homotopy involutions of 3-manifolds to involutions, Topology, to appear.
W.-C. Hsiang and R. W. Sharpe, Parameterized surgery and pseudoisotopy, Pac. J. Math. 67 (1976), 401–459.
M. Kervaire and J. Milnor, Groups of homotopy spheres, Ann. of Math. 78 (1973), 514–537.
R. C. Kirby and L. Siebenmann, On the triangulation of manifolds and the Hauptvermutung, Bull. Amer. Math. Soc. 75 (1969), 742–749.
R. Lashof, The immersion approach to triangulation and smoothing, Proc. Sympos. Pur Math. 22, 131–164. American Mathematical Society, Providence, 1971.
W. J. LeVeque, Topics in Number Theory, Vol. I. Addison-Wesley, Reading, Mass. 1956.
P. Löffler, Über die G-Rahmbarigkeit von G-Homotopiesphären, Arch. Math. (Basel) 29, (1977), 629–634.
A. M. Macbeath, On a theorem of J. Nielsen, Quart. J. Math. Oxford (2) 13 (1962), 235–236.
T. Metsänkylä, Note on the distribution of irregular primes, Ann. Acad. Sci. Fenn. Ser. A I No. 492 (1971), 7pp.
H. Miller, D. Ravenel, and W. S. Wilson, Periodic phenomena in the Adams-Novikov spectral sequence, Ann. of Math. 106 (1977), 469–516.
J. Nielsen, Abbildungsklassen endlicher Ordnung, Acta. Math. 75 (1943), 23–115.
S. Oka, The stable homotopy groups of spheres I, Hiroshima Math. J. 1 (1971), 305–337.
F. Raymond and L. Scott, The failure of Nielsen's theorem in higher dimension, Arch. Math. (Basel), to appear.
R. Schultz, Composition constructions on diffeomorphisms of Sp × Sq, Pac. J. Math. 42 (1972), 739–754.
_____, Differentiable group actions on homotopy spheres: I, Invent. Math. 31 (1975), 105–128.
_____, ibid. II, to appear.
_____, Smooth actions of small groups on exotic spheres, Proc. Sympos. Pure Math. 32, 491–496. American Mathematical Society, Providence, 1978.
_____, Spherelike G-manifolds with exotic equivariant tangent bundles, to appear in Studies in Alg.Top.(Academic Press).
_____, Finding equivariantly framed group actions on homotopy spheres, to appear.
L. Smith, Realizing complex bordism modules IV, Amer. J. Math. 99 (1977), 418–436.
R. Stong, Notes on Cobordism Theory, Mathematical Notes No. 7. Princeton University Press, Princeton, 1968.
D. Sullivan, Geometric TopologyI-Localization, Periodicity, and Galois Symmetry, multi-copied notes, MIT, 1970.
M. Tangora, Some homotopy groups mod 3, Reunion Sobre Teoria de Homotopia (Northwestern 1974), Notas de Matemáticas y Simposia No. 1, 227–246. Sociedad Matemática Mexicana, México, D. F., 1975.
H. Toda, p-primary components of homotopy groups IV., Mem. Coll. Sci. Kyoto Univ. 32 (1959), 297–332.
C. T. C. Wall, Surgery on Compact Manifolds, London Math. Soc. Monographs No. 1. Academic Press, New York, 1970.
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Schultz, R. (1979). Isotopy classes of periodic diffeomorphisms on spheres. In: Hoffman, P., Snaith, V. (eds) Algebraic Topology Waterloo 1978. Lecture Notes in Mathematics, vol 741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062148
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