𝐺-transversality revisited

Costenoble, S. R.; Waner, S.

doi:10.1090/S0002-9939-1992-1127138-3

$G$-transversality revisited
HTML articles powered by AMS MathViewer

by S. R. Costenoble and S. Waner PDF

Proc. Amer. Math. Soc. 116 (1992), 535-546 Request permission

Abstract:

We express the obstruction to $G$-transversality in two related ways: as an element in the quotient of homotopical equivariant normal bordism by geometric bordism and also as the obstruction in a homotopy lifting problem. In both cases, our formulation is given in terms of the initial data only, in contrast to earlier theories. We also obtain related obstructions to equivariant "near" transversality, i.e., transversality using arbitrarily small homotopies.

References

William Browder, Surgery on simply-connected manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 65, Springer-Verlag, New York-Heidelberg, 1972. MR 0358813, DOI 10.1007/978-3-642-50020-6
Theodor Bröcker and Edward C. Hook, Stable equivariant bordism, Math. Z. 129 (1972), 269–277. MR 321119, DOI 10.1007/BF01187353
S. R. Costenoble and S. Waner, The equivariant Spivak normal bundle and equivariant surgery, Michigan Math. J. 39 (1992), no. 3, 415–424. MR 1182497, DOI 10.1307/mmj/1029004596
Tammo tom Dieck, Bordism of $G$-manifolds and integrality theorems, Topology 9 (1970), 345–358. MR 266241, DOI 10.1016/0040-9383(70)90058-3
L. G. Lewis Jr., J. P. May, M. Steinberger, and J. E. McClure, Equivariant stable homotopy theory, Lecture Notes in Mathematics, vol. 1213, Springer-Verlag, Berlin, 1986. With contributions by J. E. McClure. MR 866482, DOI 10.1007/BFb0075778
I. Moerdijk and J.-A. Svensson, The equivariant Serre spectral sequence, Proc. Amer. Math. Soc. 118 (1993), no. 1, 263–278. MR 1123662, DOI 10.1090/S0002-9939-1993-1123662-9
Jesper Michael Møller, On equivariant function spaces, Pacific J. Math. 142 (1990), no. 1, 103–119. MR 1038731, DOI 10.2140/pjm.1990.142.103
Ted Petrie, Pseudoequivalences of $G$-manifolds, Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976) Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc., Providence, R.I., 1978, pp. 169–210. MR 520505
C. T. C. Wall, Surgery on compact manifolds, London Mathematical Society Monographs, No. 1, Academic Press, London-New York, 1970. MR 0431216
Arthur G. Wasserman, Equivariant differential topology, Topology 8 (1969), 127–150. MR 250324, DOI 10.1016/0040-9383(69)90005-6