Epsilon Nielsen fixed point theory
<p/> <p>Let <inline-formula><graphic file="1687-1812-2006-29470-i1.gif"/></inline-formula> be a map of a compact, connected Riemannian manifold, with or without boundary. For <inline-formula><graphic file="1687-1812-2006-29470-i2.gif"/>&l...
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
SpringerOpen
2006
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/26cdabb7468f445fb36fa5f37e435c03 |
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| Sumario: | <p/> <p>Let <inline-formula><graphic file="1687-1812-2006-29470-i1.gif"/></inline-formula> be a map of a compact, connected Riemannian manifold, with or without boundary. For <inline-formula><graphic file="1687-1812-2006-29470-i2.gif"/></inline-formula> sufficiently small, we introduce an <inline-formula><graphic file="1687-1812-2006-29470-i3.gif"/></inline-formula>-Nielsen number <inline-formula><graphic file="1687-1812-2006-29470-i4.gif"/></inline-formula> that is a lower bound for the number of fixed points of all self-maps of <inline-formula><graphic file="1687-1812-2006-29470-i5.gif"/></inline-formula> that are <inline-formula><graphic file="1687-1812-2006-29470-i6.gif"/></inline-formula>-homotopic to <inline-formula><graphic file="1687-1812-2006-29470-i7.gif"/></inline-formula>. We prove that there is always a map <inline-formula><graphic file="1687-1812-2006-29470-i8.gif"/></inline-formula> that is <inline-formula><graphic file="1687-1812-2006-29470-i9.gif"/></inline-formula>-homotopic to <inline-formula><graphic file="1687-1812-2006-29470-i10.gif"/></inline-formula> such that <inline-formula><graphic file="1687-1812-2006-29470-i11.gif"/></inline-formula> has exactly <inline-formula><graphic file="1687-1812-2006-29470-i12.gif"/></inline-formula> fixed points. We describe procedures for calculating <inline-formula><graphic file="1687-1812-2006-29470-i13.gif"/></inline-formula> for maps of <inline-formula><graphic file="1687-1812-2006-29470-i14.gif"/></inline-formula>-manifolds.</p> |
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