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In mathematics, the fixed-point index is a concept in topological fixed-point theory, and in particular Nielsen theory. The fixed-point index can be thought of as a multiplicity measurement for fixed points. The index can be easily defined in the setting of complex analysis: Let f(z) be a holomorphic mapping on the complex plane, and let z0 be a fixed point of f. Then the function f(z) − z is holomorphic, and has an isolated zero at z0. We define the fixed-point index of f at z0, denoted i(f, z0), to be the multiplicity of the zero of the function f(z) − z at the point z0.

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rdfs:label	Fixed-point index (en)
rdfs:comment	In mathematics, the fixed-point index is a concept in topological fixed-point theory, and in particular Nielsen theory. The fixed-point index can be thought of as a multiplicity measurement for fixed points. The index can be easily defined in the setting of complex analysis: Let f(z) be a holomorphic mapping on the complex plane, and let z0 be a fixed point of f. Then the function f(z) − z is holomorphic, and has an isolated zero at z0. We define the fixed-point index of f at z0, denoted i(f, z0), to be the multiplicity of the zero of the function f(z) − z at the point z0. (en)
sameAs	Fixed-point index
dbp:wikiPageUsesTemplate	dbt:ISBN dbt:Refimprove dbt:Reflist
Subject	Topology Fixed points (mathematics)
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Fixed-point_index?oldid=1034816393&ns=0
Wikipage page ID	2132356 (xsd:integer)
page length (characters) of wiki page	2409 (xsd:nonNegativeInteger)
Wikipage revision ID	1034816393 (xsd:integer)
Link from a Wikipage to another Wikipage	Topology Fixed points (mathematics) Lefschetz fixed-point theorem Degree of a continuous mapping Complex analysis Holomorph Solomon Lefschetz Fixed-point subgroup Heinz Hopf L. E. J. Brouwer Topology Mathematics Multiplicity (mathematics) Nielsen theory
has abstract	In mathematics, the fixed-point index is a concept in topological fixed-point theory, and in particular Nielsen theory. The fixed-point index can be thought of as a multiplicity measurement for fixed points. The index can be easily defined in the setting of complex analysis: Let f(z) be a holomorphic mapping on the complex plane, and let z0 be a fixed point of f. Then the function f(z) − z is holomorphic, and has an isolated zero at z0. We define the fixed-point index of f at z0, denoted i(f, z0), to be the multiplicity of the zero of the function f(z) − z at the point z0. In real Euclidean space, the fixed-point index is defined as follows: If x0 is an isolated fixed point of f, then let g be the function defined by Then g has an isolated singularity at x0, and maps the boundary of some deleted neighborhood of x0 to the unit sphere. We define i(f, x0) to be the Brouwer degree of the mapping induced by g on some suitably chosen small sphere around x0. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Fixed-point_index
is Wikipage redirect of	Fixed point index
is Link from a Wikipage to another Wikipage of	Lefschetz fixed-point theorem Nielsen theory Fixed point index
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Fixed-point_index

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