A note on residue formulas for the Euler class of sphere fibrations

Abstract

This paper presents a definition of residue formulas for the Euler class of cohomology-oriented sphere fibrations ζ. If the base of ζ is a topological manifold, a Hopf index theorem can be obtained and, for the smooth category, a generalization of a residue formula is derived for real vector bundles given in [2].

Keywords

Euler class / Sphere fibration / Hopf index theorem / Residue formulas

References

[1] Bott R.. Nondegenerate critical manifolds. Ann. of Math., 1954, 60: 248-261

[2] Feng H. T., Guo E. L.. A Hopf index theorem for a real vector bundle. Chin. Ann. Math., 2002, 23B(4): 507-518

[3] Spanier E. H.. Algebraic Topology, 1966, New York: McGraw Hill