Affiliation:
1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P.R. China
2. Nankai Institute of Mathematics, Nankai University, Tianjin 300071, P.R. China
Abstract
To generalize the Hopf index theorem and the Atiyah–Dupont vector fields theory, one is interested in the following problem: for a real vector bundle E over a closed manifold M with rank E = dim M, whether there exist two linearly independent cross sections of E? We provide, among others, a complete answer to this problem when both E and M are orientable. It extends the corresponding results for E = TM of Thomas, Atiyah, and Atiyah–Dupont. Moreover we prove a vanishing result of a certain mod 2 index when the bundle E admits a complex structure. This vanishing result implies many known famous results as consequences. Ideas and methods from obstruction theory, K-theory and index theory are used in getting our results.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,General Mathematics
Cited by
5 articles.
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