Displaying similar documents to “Positivity and Kleiman transversality in equivariant K -theory of homogeneous spaces”

Z k -actions fixing point ∪ Vⁿ

Pedro L. Q. Pergher (2002)

Fundamenta Mathematicae

Similarity:

We describe the equivariant cobordism classification of smooth actions ( M m , Φ ) of the group G = Z k on closed smooth m-dimensional manifolds M m 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,...

The equivariant universality and couniversality of the Cantor cube

Michael G. Megrelishvili, Tzvi Scarr (2001)

Fundamenta Mathematicae

Similarity:

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 H ( 0 , 1 ) , 0 , 1 , τ be the natural (evaluation) action of the full group of autohomeomorphisms of the Cantor cube. Then (1) there exists a topological group embedding φ : G H ( 0 , 1 ) ; (2) there exists an embedding ψ : X 0 , 1 , equivariant with respect to φ, such that ψ(X) is an equivariant retract of 0 , 1 with respect...

Commuting involutions whose fixed point set consists of two special components

Pedro L. Q. Pergher, Rogério de Oliveira (2008)

Fundamenta Mathematicae

Similarity:

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 N m is any smooth closed m-dimensional manifold with m > n and T : N m N m 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 R P 2 n , C P 2 n and H P 2 n , and the connected sum of R P 2 n and any number of copies of Sⁿ × Sⁿ, where Sⁿ is the n-sphere...

A note on the theorems of Lusternik-Schnirelmann and Borsuk-Ulam

T. E. Barros, C. Biasi (2008)

Colloquium Mathematicae

Similarity:

Let p be a prime number and X a simply connected Hausdorff space equipped with a free p -action generated by f p : X X . Let α : S 2 n - 1 S 2 n - 1 be a homeomorphism generating a free p -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 F : ( S 2 n - 1 , α ) ( X , f p ) . As applications, we derive new versions of generalized Lusternik-Schnirelmann and Borsuk-Ulam theorems.

Equivariant K-theory of flag varieties revisited and related results

V. Uma (2013)

Colloquium Mathematicae

Similarity:

We obtain several several results on the multiplicative structure constants of the T-equivariant Grothendieck ring K T ( G / B ) of the flag variety G/B. We do this by lifting the classes of the structure sheaves of Schubert varieties in K T ( G / B ) 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 K ( X ) where X denotes the wonderful compactification of the adjoint group of G, in terms of the structure...

Z k -actions with a special fixed point set

Pedro L. Q. Pergher, Rogério de Oliveira (2005)

Fundamenta Mathematicae

Similarity:

Let Fⁿ be a connected, smooth and closed n-dimensional manifold satisfying the following property: if N m is any smooth and closed m-dimensional manifold with m > n and T : N m N m is a smooth involution whose fixed point set is Fⁿ, then m = 2n. We describe the equivariant cobordism classification of smooth actions ( M m ; Φ ) of the group G = Z k on closed smooth m-dimensional manifolds M m for which the fixed point set of the action is a submanifold Fⁿ with the above property. This generalizes a result of F....

On the stratification of the orbit space for the action of automorphisms on connections

Witold Kondracki, Jan Rogulski

Similarity:

CONTENTSIntroduction..................................................................................................................................................5§1. Basic notions and notation.....................................................................................................................7  1.1. Automorphisms of principal bundles....................................................................................................7  1.2. Connections and parallel...

The centralizer of a classical group and Bruhat-Tits buildings

Daniel Skodlerack (2013)

Annales de l’institut Fourier

Similarity:

Let G be a unitary group defined over a non-Archimedean local field of odd residue characteristic and let H be the centralizer of a semisimple rational Lie algebra element of G . We prove that the Bruhat-Tits building 𝔅 1 ( H ) of H can be affinely and G -equivariantly embedded in the Bruhat-Tits building 𝔅 1 ( G ) of G so that the Moy-Prasad filtrations are preserved. The latter property forces uniqueness in the following way. Let j and j be maps from 𝔅 1 ( H ) to 𝔅 1 ( G ) which preserve the Moy–Prasad filtrations....

Non-orbit equivalent actions of 𝔽 n

Adrian Ioana (2009)

Annales scientifiques de l'École Normale Supérieure

Similarity:

For any 2 n , we construct a concrete 1-parameter family of non-orbit equivalent actions of the free group 𝔽 n . These actions arise as diagonal products between a generalized Bernoulli action and the action 𝔽 n ( 𝕋 2 , λ 2 ) , where 𝔽 n is seen as a subgroup of SL 2 ( ) .

J -invariant of linear algebraic groups

Viktor Petrov, Nikita Semenov, Kirill Zainoulline (2008)

Annales scientifiques de l'École Normale Supérieure

Similarity:

Let G be a semisimple linear algebraic group of inner type over a field F , and let X be a projective homogeneous G -variety such that G splits over the function field of X . We introduce the J -invariant of G which characterizes the motivic behavior of X , and generalizes the J -invariant defined by A. Vishik in the context of quadratic forms. We use this J -invariant to provide motivic decompositions of all generically split projective homogeneous G -varieties, e.g. Severi-Brauer varieties,...

Degree of T-equivariant maps in ℝⁿ

Joanna Janczewska, Marcin Styborski (2007)

Banach Center Publications

Similarity:

A special case of G-equivariant degree is defined, where G = ℤ₂, and the action is determined by an involution T : p q p 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 : ( , S n - 1 ) ( , 0 ) are T-homotopic iff they are gradient T-homotopic. This is an equivariant generalization of the result due to Parusiński.

Stable soliton resolution for equivariant wave maps exterior to a ball

Andrew Lawrie (2014-2015)

Séminaire Laurent Schwartz — EDP et applications

Similarity:

In this report we review the proof of the stable soliton resolution conjecture for equivariant wave maps exterior to a ball in 3 and taking values in the 3 -sphere. This is joint work with Carlos Kenig, Baoping Liu, and Wilhelm Schlag.

Varieties of minimal rational tangents of codimension 1

Jun-Muk Hwang (2013)

Annales scientifiques de l'École Normale Supérieure

Similarity:

Let  X be a uniruled projective manifold and let  x be a general point. The main result of [2] says that if the ( - K X ) -degrees (i.e., the degrees with respect to the anti-canonical bundle of  X ) of all rational curves through x are at least dim X + 1 , then X is a projective space. In this paper, we study the structure of  X when the ( - K X ) -degrees of all rational curves through x are at least dim X . Our study uses the projective variety 𝒞 x T x ( X ) , called the VMRT at  x , defined as the union of tangent directions to the...

Shadowing in actions of some Abelian groups

Sergei Yu. Pilyugin, Sergei B. Tikhomirov (2003)

Fundamenta Mathematicae

Similarity:

We study shadowing properties of continuous actions of the groups p and p × p . Necessary and sufficient conditions are given under which a linear action of p on m has a Lipschitz shadowing property.

Obstruction sets and extensions of groups

Francesca Balestrieri (2016)

Acta Arithmetica

Similarity:

Let X be a nice variety over a number field k. We characterise in pure “descent-type” terms some inequivalent obstruction sets refining the inclusion X ( k ) é t , B r X ( k ) B r . In the first part, we apply ideas from the proof of X ( k ) é t , B r = X ( k ) k by Skorobogatov and Demarche to new cases, by proving a comparison theorem for obstruction sets. In the second part, we show that if k are such that E x t ( , k ) , then X ( k ) = X ( k ) . This allows us to conclude, among other things, that X ( k ) é t , B r = X ( k ) k and X ( k ) S o l , B r = X ( k ) S o l k .

The Brauer group and the Brauer–Manin set of products of varieties

Alexei N. Skorobogatov, Yuri G. Zahrin (2014)

Journal of the European Mathematical Society

Similarity:

Let X and Y be smooth and projective varieties over a field k finitely generated over Q , and let X ¯ and Y ¯ be the varieties over an algebraic closure of k obtained from X and Y , respectively, by extension of the ground field. We show that the Galois invariant subgroup of Br ( X ¯ ) Br( Y ¯ ) has finite index in the Galois invariant subgroup of Br ( X ¯ × Y ¯ ) . This implies that the cokernel of the natural map Br ( X ) Br ( Y ) Br ( X × Y ) is finite when k is a number field. In this case we prove that the Brauer–Manin set of the...

Springer fiber components in the two columns case for types A and D are normal

Nicolas Perrin, Evgeny Smirnov (2012)

Bulletin de la Société Mathématique de France

Similarity:

We study the singularities of the irreducible components of the Springer fiber over a nilpotent element N with N 2 = 0 in a Lie algebra of type A or D (the so-called two columns case). We use Frobenius splitting techniques to prove that these irreducible components are normal, Cohen–Macaulay, and have rational singularities.

Stabilization of monomial maps in higher codimension

Jan-Li Lin, Elizabeth Wulcan (2014)

Annales de l’institut Fourier

Similarity:

A monomial self-map f on a complex toric variety is said to be k -stable if the action induced on the 2 k -cohomology is compatible with iteration. We show that under suitable conditions on the eigenvalues of the matrix of exponents of f , we can find a toric model with at worst quotient singularities where f is k -stable. If f is replaced by an iterate one can find a k -stable model as soon as the dynamical degrees λ k of f satisfy λ k 2 > λ k - 1 λ k + 1 . On the other hand, we give examples of monomial maps f , where...

Explicit computations of all finite index bimodules for a family of II 1 factors

Stefaan Vaes (2008)

Annales scientifiques de l'École Normale Supérieure

Similarity:

We study II 1 factors M and N associated with good generalized Bernoulli actions of groups having an infinite almost normal subgroup with the relative property (T). We prove the following rigidity result : every finite index M - N -bimodule (in particular, every isomorphism between M and N ) is described by a commensurability of the groups involved and a commensurability of their actions. The fusion algebra of finite index M - M -bimodules is identified with an extended Hecke fusion algebra,...