Involutions with 𝑊(𝐹)=1

Lü, Zhi

doi:10.1090/S0002-9939-99-05252-1

Involutions with $W(F)=1$
HTML articles powered by AMS MathViewer

by Zhi Lü PDF

Proc. Amer. Math. Soc. 128 (2000), 307-313 Request permission

Abstract:

Let $(T,M^n)$ be a smooth involution on a closed $n$-dimensional manifold such that all Stiefel-Whitney classes of the tangent bundle to each component of the fixed point set $F$ of $(T,M^n)$ vanish in positive dimension. In this paper, we estimate the least possible lower bound of dim$F$ if $(T,M^n)$ does not bound.

References

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
P. E. Conner and E. E. Floyd, Fibring within a cobordism class, Michigan Math. J. 12 (1965), 33–47. MR 179796
Pierre E. Conner, Differentiable periodic maps, 2nd ed., Lecture Notes in Mathematics, vol. 738, Springer, Berlin, 1979. MR 548463
Czes Kosniowski and R. E. Stong, Involutions and characteristic numbers, Topology 17 (1978), no. 4, 309–330. MR 516213, DOI 10.1016/0040-9383(78)90001-0
Robert E. Stong, Notes on cobordism theory, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1968. Mathematical notes. MR 0248858
J. M. Boardman, On manifolds with involution, Bull. Amer. Math. Soc. 73 (1967), 136–138. MR 205260, DOI 10.1090/S0002-9904-1967-11683-5