Bordism classes of vector bundles over real projective spaces

Torrence, Bruce F.

doi:10.1090/S0002-9939-1993-1136239-6

Bordism classes of vector bundles over real projective spaces
HTML articles powered by AMS MathViewer

by Bruce F. Torrence PDF

Proc. Amer. Math. Soc. 118 (1993), 963-969 Request permission

Abstract:

A basis is presented for the ${\mathbf {R}}{{\mathbf {P}}^n}$ classes in ${\mathfrak {N}_n}(BO)$. This basis is used to prove that every smooth involution $(M,T)$ on a closed manifold bounds if its fixed point set is a disjoint union of odd-dimensional projective spaces of constant dimension.

References

Frank L. Capobianco, Stationary points of $(Z_{2})^{k}$-actions, Proc. Amer. Math. Soc. 61 (1976), no. 2, 377–380 (1977). MR 425993, DOI 10.1090/S0002-9939-1976-0425993-4
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
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
David C. Royster, Involutions fixing the disjoint union of two projective spaces, Indiana Univ. Math. J. 29 (1980), no. 2, 267–276. MR 563211, DOI 10.1512/iumj.1980.29.29018
R. E. Stong, Involutions fixing projective spaces, Michigan Math. J. 13 (1966), 445–447. MR 206979