About: Lefschetz fixed-point theorem

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In mathematics, the Lefschetz fixed-point theorem is a formula that counts the fixed points of a continuous mapping from a compact topological space to itself by means of traces of the induced mappings on the homology groups of . It is named after Solomon Lefschetz, who first stated it in 1926. The counting is subject to an imputed multiplicity at a fixed point called the fixed-point index. A weak version of the theorem is enough to show that a mapping without any fixed point must have rather special topological properties (like a rotation of a circle).

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rdf:type	Thing agent
rdfs:label	Lefschetz fixed-point theorem (en)
rdfs:comment	In mathematics, the Lefschetz fixed-point theorem is a formula that counts the fixed points of a continuous mapping from a compact topological space to itself by means of traces of the induced mappings on the homology groups of . It is named after Solomon Lefschetz, who first stated it in 1926. The counting is subject to an imputed multiplicity at a fixed point called the fixed-point index. A weak version of the theorem is enough to show that a mapping without any fixed point must have rather special topological properties (like a rotation of a circle). (en)
sameAs	Lefschetz fixed-point theorem Lefschetz fixed-point theorem
dbp:wikiPageUsesTemplate	dbt:Authority_control dbt:Cite_journal dbt:Harv dbt:Reflist dbt:Short_description dbt:Springer
Subject	Continuous mappings Fixed-point theorems Theorems in algebraic topology
gold:hypernym	Formula
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Lefschetz_fixed-point_theorem?oldid=1066620096&ns=0
Wikipage page ID	582530 (xsd:integer)
page length (characters) of wiki page	8845 (xsd:nonNegativeInteger)
Wikipage revision ID	1066620096 (xsd:integer)
Link from a Wikipage to another Wikipage	Unit disk Algebraic stack Annals of Mathematics Betti number Brouwer fixed-point theorem CW complex Continuous mappings Fixed-point theorems Lefschetz zeta function Triangulation (topology) Cohomology Coincidence point Compact space Continuous function Holomorphic Lefschetz fixed-point formula Homology (mathematics) Homotopy Solomon Lefschetz Equidimensionality Fixed-point index Fixed-point theorems Fixed-point subgroup Frobenius endomorphism Identity function Manifold Trace (linear algebra) Transactions of the American Mathematical Society Euler characteristic Topological space Mathematics Multiplicity (mathematics) Poincaré duality Poincaré–Hopf theorem Rational number Simplicial approximation theorem Simplicial homology Simplicial map Singular homology Theorems in algebraic topology
has abstract	In mathematics, the Lefschetz fixed-point theorem is a formula that counts the fixed points of a continuous mapping from a compact topological space to itself by means of traces of the induced mappings on the homology groups of . It is named after Solomon Lefschetz, who first stated it in 1926. The counting is subject to an imputed multiplicity at a fixed point called the fixed-point index. A weak version of the theorem is enough to show that a mapping without any fixed point must have rather special topological properties (like a rotation of a circle). (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Lefschetz_fixed-point_theorem
is Wikipage redirect of	Lefshetz fixed-point theorem Grothendieck-Lefschetz formula Grothendieck–Lefschetz formula Lefschetz-Hopf theorem Lefschetz fixed-point formula Lefschetz fixed point formula Lefschetz fixed point theorem Lefschetz fixed point theorm Lefschetz number Lefschetz trace formula Lefschetz–Hopf theorem Lefshetz fixed point formula Lefshetz number Lefshetz trace formula
is Link from a Wikipage to another Wikipage of	Grothendieck trace formula List of theorems Local zeta function Möbius transformation Nonlinear functional analysis Adolf Hurwitz Algebraic topology Artin–Mazur zeta function Atiyah–Bott fixed-point theorem Atiyah–Singer index theorem Brauer's theorem on induced characters Brouwer fixed-point theorem Categorical trace Glossary of algebraic topology Glossary of arithmetic and diophantine geometry Lefschetz duality Lefschetz zeta function Lefshetz fixed-point theorem Michael Atiyah Christopher Deninger Hurwitz's automorphisms theorem Jörg Bewersdorff Coincidence point Holomorphic Lefschetz fixed-point formula List of algebraic topology topics

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