Transactions of the American Mathematical Society · 1983 · 143 citations · 6 references
Mathematical ProgrammingMath XmlnsFixed Point SetsCanonical MethodEngineeringRepresentation TheoryLie GroupAnnotation Encoding=Discrete Dynamical SystemExtremal Set TheoryEducationDiscrete MathematicsLie Point SymmetryLie TheoryLie AlgebraStability
Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding="application/x-tex">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a compact Lie group. A canonical method is given for constructing a <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding="application/x-tex">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-space from homotopy theoretic information about its fixed point sets. The construction is a special case of the categorical bar construction. Applications include easy constructions of certain classifying spaces, as well as <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding="application/x-tex">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-Eilenberg-Mac Lane spaces and Postnikov towers.
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