Displaying similar documents to “Equivariant algebraic topology”

Classification of homotopy classes of equivariant gradient maps

E. N. Dancer, K. Gęba, S. M. Rybicki (2005)

Fundamenta Mathematicae

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Let V be an orthogonal representation of a compact Lie group G and let S(V),D(V) be the unit sphere and disc of V, respectively. If F: V → ℝ is a G-invariant C¹-map then the G-equivariant gradient C⁰-map ∇F: V → V is said to be admissible provided that ( ∇ F ) - 1 ( 0 ) ∩ S ( V ) = ∅ . We classify the homotopy classes of admissible G-equivariant gradient maps ∇F: (D(V),S(V)) → (V,V∖0).

On equivariant deformations of maps.

Antonio Vidal (1988)

Publicacions Matemàtiques

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We work in the smooth category: manifolds and maps are meant to be smooth. Let G be a finite group acting on a connected closed manifold X and f an equivariant self-map on X with f|A fixpointfree, where A is a closed invariant submanifold of X with codim A ≥ 3. The purpose of this paper is to give a proof using obstruction theory of the following fact: If X is simply connected and the action of G on X - A is free, then f is equivariantly deformable rel. A to fixed...

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.