The oriented bordism of 𝑍_{2^{𝑘}} actions

Wheeler, E. R.

doi:10.1090/S0002-9947-1974-0356097-X

The oriented bordism of $Z_{2^{k}}$ actions
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by E. R. Wheeler

Trans. Amer. Math. Soc. 199 (1974), 113-121

DOI: https://doi.org/10.1090/S0002-9947-1974-0356097-X

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Abstract:

Let ${R_2}$ be the subring of the rationals given by ${R_2} = Z[1/2]$. It is shown that for $G = {Z_{{2^k}}}$ the bordism group of orientation preserving $G$ actions on oriented manifolds tensored with ${R_2}$ is a free ${\Omega _ \ast } \otimes {R_2}$ module on even dimensional generators (where ${\Omega _ \ast }$ is the oriented bordism ring).

References

M. F. Atiyah, Bordism and cobordism, Proc. Cambridge Philos. Soc. 57 (1961), 200–208. MR 126856, DOI 10.1017/s0305004100035064
M. F. Atiyah, $K$-theory, W. A. Benjamin, Inc., New York-Amsterdam, 1967. Lecture notes by D. W. Anderson. MR 0224083
Pierre E. Conner, Lectures on the action of a finite group, Lecture Notes in Mathematics, No. 73, Springer-Verlag, Berlin-New York, 1968. MR 0258023, DOI 10.1007/BFb0079602
P. E. Conner and E. E. Floyd, Differentiable periodic maps, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 33, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg, 1964. MR 0176478

Periodic maps via Smith theory

Katsuhiro Komiya, Oriented bordism and involutions, Osaka Math. J. 9 (1972), 165–181. MR 307221
Peter S. Landweber, Equivariant bordism and cyclic groups, Proc. Amer. Math. Soc. 31 (1972), 564–570. MR 296969, DOI 10.1090/S0002-9939-1972-0296969-1
Erich Ossa, Unitary bordism of abelian groups, Proc. Amer. Math. Soc. 33 (1972), 568–571. MR 293666, DOI 10.1090/S0002-9939-1972-0293666-3
H. L. Rosenzweig, Bordism of involutions on manifolds, Illinois J. Math. 16 (1972), 1–10. MR 290386, DOI 10.1215/ijm/1256052378
R. E. Stong, Complex and oriented equivariant bordism, Topology of Manifolds (Proc. Inst., Univ. of Georgia, Athens, Ga., 1969) Markham, Chicago, Ill., 1970, pp. 291–316. MR 0273644
Robert E. Stong, Notes on cobordism theory, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1968. Mathematical notes. MR 0248858
R. E. Stong, Unoriented bordism and actions of finite groups, Memoirs of the American Mathematical Society, No. 103, American Mathematical Society, Providence, R.I., 1970. MR 0273645

The oriented bordism of cyclic, group actions