On the index ofG-spaces

DOI10.1070/SM2000v191n09ABEH000504zbMath0987.57016OpenAlexW2137215716MaRDI QIDQ2710722

Alexey Volovikov

Publication date: 3 October 2001

Published in: Sbornik: Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/sm2000v191n09abeh000504

zbMATH Keywords

critical pointsBorel cohomologyLeray spectral sequenceBourgin-Yang theorem\(G\)-categoryideal-valued indexpartial coincidences

Mathematics Subject Classification ID

Lyusternik-Shnirel'man category of a space, topological complexity à la Farber, topological robotics (topological aspects) (55M30) Classifying spaces of groups and (H)-spaces in algebraic topology (55R35) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Equivariant homology and cohomology in algebraic topology (55N91) Fixed points and coincidences in algebraic topology (55M20) Homology of classifying spaces and characteristic classes in algebraic topology (55R40) Equivariant homotopy theory in algebraic topology (55P91) Compact groups of homeomorphisms (57S10)

Related Items (24)

The genus and the category of configuration spaces ⋮ On the Cohen-Lusk theorem ⋮ FREE ACTION OF FINITE GROUPS ON SPACES OF COHOMOLOGY TYPE (0, b) ⋮ The Schwarz genus of the Stiefel manifold ⋮ On the existence of \(G\)-equivariant maps ⋮ Cohomology algebra of orbit spaces of free involutions on the product of projective space and 4-sphere ⋮ A topological central point theorem ⋮ Colored Tverberg theorem with new constraints on the faces ⋮ Configuration-like spaces and coincidences of maps on orbits ⋮ Vanishing of all equivariant obstructions and the mapping degree ⋮ Borsuk-Ulam theorems and their parametrized versions for \(\mathbb {F}P^m\times \mathbb {S}^3\) ⋮ The genus of \(G\)-spaces and topological lower bounds for chromatic numbers of hypergraphs ⋮ Finite-to-one maps ⋮ Index of Grassmann manifolds and orthogonal shadows ⋮ A Borsuk-Ulam type theorem for the product of a projective space and 3-sphere ⋮ Coincidences for maps of spaces with finite group actions ⋮ Knaster's problem for almost \((\mathbb Z_p)^k\)-orbits ⋮ General Bourgin-Yang theorems ⋮ Fixed point free actions of spheres and equivariant maps ⋮ FREE ACTIONS OF SOME COMPACT GROUPS ON MILNOR MANIFOLDS ⋮ CUTTING A PART FROM MANY MEASURES ⋮ Indices of a finitistic space with \(\bmod 2\) cohomology \(\mathbb{R} P^n \times \mathbb{S}^2\) ⋮ Equivariant topology of configuration spaces ⋮ Borsuk-Ulam type theorems for \(G\)-spaces with applications to Tucker type lemmas

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