Displaying similar documents to “Classification of homotopy classes of equivariant gradient maps”

Degree of T-equivariant maps in ℝⁿ

Joanna Janczewska, Marcin Styborski (2007)

Banach Center Publications

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A special case of G-equivariant degree is defined, where G = ℤ₂, and the action is determined by an involution T : ℝ p ⊕ ℝ q → ℝ p ⊕ ℝ q given by T(u,v) = (u,-v). The presented construction is self-contained. It is also shown that two T-equivariant gradient maps f , g : ( ℝ ⁿ , S n - 1 ) → ( ℝ ⁿ , ℝ ⁿ ∖ 0 ) are T-homotopic iff they are gradient T-homotopic. This is an equivariant generalization of the result due to Parusiński.

Equivariant algebraic topology

Sören Illman (1973)

Annales de l'institut Fourier

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Let G be a topological group. We give the existence of an equivariant homology and cohomology theory, defined on the category of all G -pairs and G -maps, which both satisfy all seven equivariant Eilenberg-Steenrod axioms and have a given covariant and contravariant, respectively, coefficient system as coefficients. In the case that G is a compact Lie group we also define equivariant C W -complexes and mention some of their basic properties. The paper is a short abstract...

Equivariant measurable liftings

Nicolas Monod (2015)

Fundamenta Mathematicae

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We discuss equivariance for linear liftings of measurable functions. Existence is established when a transformation group acts amenably, as e.g. the Möbius group of the projective line. Since the general proof is very simple but not explicit, we also provide a much more explicit lifting for semisimple Lie groups acting on their Furstenberg boundary, using unrestricted Fatou convergence. This setting is relevant to L ∞ -cocycles for characteristic classes.