Pacific Journal of Mathematics

The eta invariant, ${\rm Pin}^c$ bordism, and equivariant ${\rm Spin}^c$ bordism for cyclic $2$-groups.

Anthony Bahri and Peter Gilkey

Article information

Source
Pacific J. Math., Volume 128, Number 1 (1987), 1-24.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102699433

Mathematical Reviews number (MathSciNet)
MR883375

Zentralblatt MATH identifier
0587.58045

Subjects
Primary: 57R90: Other types of cobordism [See also 55N22]
Secondary: 58G10

Citation

Bahri, Anthony; Gilkey, Peter. The eta invariant, ${\rm Pin}^c$ bordism, and equivariant ${\rm Spin}^c$ bordism for cyclic $2$-groups. Pacific J. Math. 128 (1987), no. 1, 1--24. https://projecteuclid.org/euclid.pjm/1102699433


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References

  • [1] D. W. Anderson, E. H. Brown and F. P. Peterson, Spin cobordism, Bull. Amer. Math. Soc, 72 (1966), 257-260.
  • [2] M. F. Atiyah, K-theory, W. A. Benjamin (1967).
  • [3] M. F. Atiyah, R. Bott and A. Shapiro, Clifford Modules, Topology, 3 Supp 1 (1964), 3-38.
  • [4] M. Atiyah, V. K. Patodi and I. M. Singer, Spectral asymmetry and Riemannian Geometry I, Math. Proc. Camb. Phil. Soc, 77 (1975), 43-69. II Math. Proc. Camb. Phil. Soc, 78 (1975), 405-432. Ill Math. Proc. Camb. Phil. Soc, 79 (1976), 71-99.
  • [5] A. Bahri and P. Gilkey, Pinc bordism and equiariant Spinc bordism of cyclic 2-groups,(to appear Proc. Amer. Math. Soc).
  • [6] H. Cartan and S. Eilenberg, Homological Algebra, (1956), Princeton
  • [7] P. E. Conner and E. E. Floyd, Differentiate Periodic Maps, Springer Verlag 1964.
  • [8] J. F. Davis and R. J. Milgram, A survey of the Spherical Space form Problem, Mathematical Reports, 2 (1984), 223-283. (Harwood Academic Publishers).
  • [9] K. Fujii, T. Kobayashi, K. Shimomura, and M. Sugawara, KO-groups of lens spaces modulo powers of two, Hiroshima Math. J, 8 (1978), 469-489. Indiana Univ. Math. J, 27 (1978), 889-918.
  • [10] V. Giambalvo, Pin and Pin' cobordism, Proc. Amer. Math. Soc, 39 (1973), 395-401.
  • [11] P. Gilkey, The eta invariant for even dimensional Pinc manifolds, Advances in Math, 58 (1985), 243-284.
  • [12] P. Gilkey, The eta invariant and the K-theory of spherical space forms, Inventiones Math, 76 (1984), 421-453.
  • [13] P. Gilkey, The eta invariant and equivariant unitary bordism for spherical space form groups, (to appear).
  • [14] P. Gilkey, Invariance Theory, The Heat Equation, and the Atiyah-Singer Index Theo- rem, Publish or Perish Press (1985).
  • [15] N. Hitchin, Harmonic spinors, Advances in Math, 14 (1974), 1-55.
  • [16] U. Korschorke, Concordanceand bordism of linefields, Inventiones Math, 24 (1974), 241-268.
  • [17] F. P. Peterson, Lectures on cobordism theory, Lecture notes in mathematics, Kyoto University (1968).
  • [18] R. E. Stong, Relations among characteristic numbers I, Topology, 4 (1965), 267-286. II Topology, 5 (1966), 133-148.
  • [19] R. E. Stong, Notes on Cobordism, Princeton University Press (1968).
  • [20] G. Wilson, K-theory invariants for unitary G-bordism, Quart J. Math, 24 (1973), 499-526.
  • [21] J. A. Wolf, Spaces of Constant Curvature, Publish or Perish Press, 5th ed (1984).