• Corpus ID: 18360278

THE POINCARÉ-HOPF THEOREM

@inproceedings{Wright2008THEPT,
  title={THE POINCARÉ-HOPF THEOREM},
  author={Alex Wright and Kael Dixon},
  year={2008}
}
In this paper, we will introduce the reader to the field of topology given a background of Calculus and Analysis. To familiarize the reader with topological concepts, we will present a proof of Brouwer’s Fixed Point Theorem. The end result of this paper will be a proof of the Poincaré-Hopf Theorem, an important theorem equating the index of a vector field on a manifold, and the Euler characteristic, an invariant of the manifold itself. We will conclude this paper with some useful applications… 
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