Search results for: HOPF THEOREM

• The Hopf theorem for gradient local vector fields on manifolds

  Publication

  • P. Bartłomiejczyk
  • P. Nowak-Przygodzki

  - New York Journal of Mathematics - Year 2015

  We prove the Hopf theorem for gradient local vector fields on manifolds, i.e., we show that there is a natural bijection between the set of gradient otopy classes of gradient local vector fields and the integers if the manifold is connected Riemannian without boundary.

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• A Hopf type theorem for equivariant local maps

  Publication

  • P. Bartłomiejczyk

  - Colloquium Mathematicum - Year 2017

  We study otopy classes of equivariant local maps and prove a Hopf type theorem for such maps in the case of a real finite-dimensional orthogonal representation of a compact Lie group.

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• The Hopf type theorem for equivariant gradient local maps

  Publication

  • P. Bartłomiejczyk
  • P. Nowak-Przygodzki

  - Journal of Fixed Point Theory and Applications - Year 2017

  We construct a degree-type otopy invariant for equivariant gradient local maps in the case of a real finite-dimensional orthogonal representation of a compact Lie group. We prove that the invariant establishes a bijection between the set of equivariant gradient otopy classes and the direct sum of countably many copies of Z.

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