Concentrated cyclic actions of high periodicity
Daniel Berend and Gabriel Katz
Trans. Amer. Math. Soc. 323 (1991), 665-689
Primary 57S17; Secondary 57R20, 57S15, 58G10
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Abstract: The class of concentrated periodic diffeomorphisms is introduced. A diffeomorphism is called concentrated if, roughly speaking, its normal eigenvalues range in a small (with respect to the period of and the dimension of ) arc on the circle. In many ways, the cyclic action generated by such a behaves on the one hand as a circle action and on the other hand as a generic prime power order cyclic action. For example, as for circle actions, , provided that the left-hand side is an integer; as for prime power order actions, cannot have a single fixed point if is closed. A variety of integrality results, relating to the usual signatures of certain characteristic submanifolds of the regular neighbourhood of in to via the normal -representations, is established.
P. Alexander and Gary
C. Hamrick, Periodic maps on Poincaré duality spaces,
Comment. Math. Helv. 53 (1978), no. 1, 149–159.
F. Atiyah and I.
M. Singer, The index of elliptic operators. III, Ann. of Math.
(2) 87 (1968), 546–604. MR 0236952
Berend and Gabriel
Katz, Separating topology and number theory in the Atiyah-Singer
𝑔-signature formula, Duke Math. J. 61 (1990),
no. 3, 939–971. MR 1084466
Hirzebruch, Topological methods in algebraic geometry, Third
enlarged edition. New appendix and translation from the second German
edition by R. L. E. Schwarzenberger, with an additional section by A.
Borel. Die Grundlehren der Mathematischen Wissenschaften, Band 131,
Springer-Verlag New York, Inc., New York, 1966. MR 0202713
Kawakubo and Frank
Raymond, The index of manifolds with toral actions and geometric
interpretations of the
𝜎(∞,(𝑆¹,𝑀ⁿ)) invariant of Atiyah
and Singer, (Univ. Massachusetts, Amherst, Mass., 1971) Springer,
Berlin, 1972, pp. 228–233. Lecture Notes in Math., Vol. 298. MR 0358840
- J. P. Alexander and G. C. Hamrick, Periodic maps on Poincaré duality spaces, Comment. Math Helv. 53 (1978), 149-159. MR 483537 (80a:57016)
- M. F. Atiyah and I. M. Singer, The index of elliptic operators. III, Ann. of Math. 87 (1968), 546-604. MR 0236952 (38:5245)
- D. Berend and G. Katz, Separating topology and number theory in the Atiyah-Singer -signature formula, Duke Math. J. 61 (1990). MR 1084466 (91k:58122)
- F. Hirzebruch, Topological methods in algebraic geometry, Springer-Verlag, New York, 1966. MR 0202713 (34:2573)
- K. Kawakubo and F. Raymond, The index of manifolds with toral actions and geometric interpretations of the -invariant of Atiyah and Singer, Lecture Notes in Math., vol. 298, Springer-Verlag, pp. 228-233. MR 0358840 (50:11299)
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