Displaying similar documents to “Equivariant algebraic topology”

Equivariant one-parameter deformations of associative algebra morphisms

Raj Bhawan Yadav (2023)

Czechoslovak Mathematical Journal

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We introduce equivariant formal deformation theory of associative algebra morphisms. We also present an equivariant deformation cohomology of associative algebra morphisms and using this we study the equivariant formal deformation theory of associative algebra morphisms. We discuss some examples of equivariant deformations and use the Maurer-Cartan equation to characterize equivariant deformations.

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.