An -equivariant degree and the Fuller index
Grzegorz Dylawerski, Kazimierz Gęba, Jerzy Jodel, Wacław Marzantowicz (1991)
Annales Polonici Mathematici
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Grzegorz Dylawerski, Kazimierz Gęba, Jerzy Jodel, Wacław Marzantowicz (1991)
Annales Polonici Mathematici
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Dave Anderson, Stephen Griffeth, Ezra Miller (2011)
Journal of the European Mathematical Society
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We prove the conjectures of Graham–Kumar [GrKu08] and Griffeth–Ram [GrRa04] concerning the alternation of signs in the structure constants for torus-equivariant -theory of generalized flag varieties . These results are immediate consequences of an equivariant homological Kleiman transversality principle for the Borel mixing spaces of homogeneous spaces, and their subvarieties, under a natural group action with finitely many orbits. The computation of the coefficients in the expansion...
Pedro L. Q. Pergher (2002)
Fundamenta Mathematicae
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We describe the equivariant cobordism classification of smooth actions of the group on closed smooth m-dimensional manifolds for which the fixed point set of the action is the union F = p ∪ Vⁿ, where p is a point and Vⁿ is a connected manifold of dimension n with n > 0. The description is given in terms of the set of equivariant cobordism classes of involutions fixing p ∪ Vⁿ. This generalizes a lot of previously obtained particular cases of the above question; additionally,...
Andrew Lawrie (2014-2015)
Séminaire Laurent Schwartz — EDP et applications
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In this report we review the proof of the stable soliton resolution conjecture for equivariant wave maps exterior to a ball in and taking values in the -sphere. This is joint work with Carlos Kenig, Baoping Liu, and Wilhelm Schlag.
Michael G. Megrelishvili, Tzvi Scarr (2001)
Fundamenta Mathematicae
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Let ⟨G,X,α⟩ be a G-space, where G is a non-Archimedean (having a local base at the identity consisting of open subgroups) and second countable topological group, and X is a zero-dimensional compact metrizable space. Let be the natural (evaluation) action of the full group of autohomeomorphisms of the Cantor cube. Then (1) there exists a topological group embedding ; (2) there exists an embedding , equivariant with respect to φ, such that ψ(X) is an equivariant retract of with respect...
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 -cocycles for characteristic classes.
Michał Sadowski (1991)
Annales Polonici Mathematici
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Aleksander Misiak, Eugeniusz Stasiak (2001)
Mathematica Bohemica
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In this note, there are determined all biscalars of a system of linearly independent contravariant vectors in -dimensional pseudo-Euclidean geometry of index one. The problem is resolved by finding a general solution of the functional equation for an arbitrary pseudo-orthogonal matrix of index one and the given vectors .
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 . We classify the homotopy classes of admissible G-equivariant gradient maps ∇F: (D(V),S(V)) → (V,V∖0).
T. E. Barros, C. Biasi (2008)
Colloquium Mathematicae
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Let p be a prime number and X a simply connected Hausdorff space equipped with a free -action generated by . Let be a homeomorphism generating a free -action on the (2n-1)-sphere, whose orbit space is some lens space. We prove that, under some homotopy conditions on X, there exists an equivariant map . As applications, we derive new versions of generalized Lusternik-Schnirelmann and Borsuk-Ulam theorems.
Ranee Brylinski (2002)
Annales de l’institut Fourier
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Let be a (generalized) flag manifold of a complex semisimple Lie group . We investigate the problem of constructing a graded star product on which corresponds to a -equivariant quantization of symbols into twisted differential operators acting on half-forms on . We construct, when is generated by the momentum functions for , a preferred choice of where has the form . Here are operators on . In the known examples, () is not a differential operator, and so the star...
V. Uma (2013)
Colloquium Mathematicae
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We obtain several several results on the multiplicative structure constants of the T-equivariant Grothendieck ring of the flag variety G/B. We do this by lifting the classes of the structure sheaves of Schubert varieties in to R(T) ⊗ R(T), where R(T) denotes the representation ring of the torus T. We further apply our results to describe the multiplicative structure constants of where X denotes the wonderful compactification of the adjoint group of G, in terms of the structure...
Pedro L. Q. Pergher, Rogério de Oliveira (2008)
Fundamenta Mathematicae
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Let Fⁿ be a connected, smooth and closed n-dimensional manifold. We call Fⁿ a manifold with property when it has the following property: if is any smooth closed m-dimensional manifold with m > n and is a smooth involution whose fixed point set is Fⁿ, then m = 2n. Examples of manifolds with this property are: the real, complex and quaternionic even-dimensional projective spaces , and , and the connected sum of and any number of copies of Sⁿ × Sⁿ, where Sⁿ is the n-sphere...
Paul F. Baum, Ludwik Dąbrowski, Piotr M. Hajac (2015)
Banach Center Publications
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Within the framework of free actions of compact quantum groups on unital C*-algebras, we propose two conjectures. The first one states that, if is a free coaction of the C*-algebra H of a non-trivial compact quantum group on a unital C*-algebra A, then there is no H-equivariant *-homomorphism from A to the equivariant join C*-algebra . For A being the C*-algebra of continuous functions on a sphere with the antipodal coaction of the C*-algebra of functions on ℤ/2ℤ, we recover the celebrated...
Sören Illman (1973)
Annales de l'institut Fourier
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Let be a topological group. We give the existence of an equivariant homology and cohomology theory, defined on the category of all -pairs and -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 is a compact Lie group we also define equivariant -complexes and mention some of their basic properties. The paper is a short abstract...