Construction of sphere maps with given degrees and a new proof of Morse index formula

Xiao-Song Yang

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arXiv · 1111.4276

Construction of sphere maps with given degrees and a new proof of Morse index formula

Xiao-Song Yang

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Abstract

This note presents a procedure of constructing a higher dimensional sphere map from a lower dimensional one and gives an explicit formula for smooth sphere map with a given degree. As an application a new proof of a generalized Poincare-Hopf theorem called Morse index formula is also presented.

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Xiao-Song Yang. 2011-11-18. Construction of sphere maps with given degrees and a new proof of Morse index formula. https://arxiv.org/abs/1111.4276

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