A configuration space for equivariant connective K-homology

Velásquez, Mario

doi:10.4171/jncg/225

Cited by 4 publications

(14 citation statements)

References 15 publications

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“…Proof. The proof is similar to given in [18] and then we give only a sketch. For this proof we need to recall the following lemma.…”

Section: Connective K-homologymentioning

confidence: 88%

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A description of the assembly map for the Baum-Connes conjecture with coefficients

Velásquez

2016

Preprint

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“…Proof. The proof is similar to given in [18] and then we give only a sketch. For this proof we need to recall the following lemma.…”

Section: Connective K-homologymentioning

confidence: 88%

“…We use that model to give a description of the analytic assembly map for the Baum-Connes conjecture with coefficients. This work is a continuation of [18], and most of the results and proofs in Section 2 are generalizations of this paper.…”

Section: Introductionmentioning

confidence: 95%

A description of the assembly map for the Baum-Connes conjecture with coefficients

Velásquez

2016

Preprint

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“…In [Vel15] and [Vel19] a configuration space representing equivariant connective K-homology for finite groups was constructed. We recall the construction briefly.…”

Section: Final Remarksmentioning

confidence: 99%

“…In order to relate H * (C(X, x 0 , G) G ; C) with F G (X) we need to recall the following result proved in Theorem 6.13 in [Vel15] using the equivariant Chern character obtained in [Lüc02].…”

Section: Final Remarksmentioning

confidence: 99%

“…This description indicates that F G (X) has the size of the Fock space of a Heisenberg superalgebra. Following ideas of [Seg96], in [Vel15] appears another reason to study F G (X). When X is a G-spin c -manifold of even dimension, F G (X) is isomorphic to the homology with complex coefficients of the G-fixed point set of a based configuration space C(X, x 0 , G) whose G-equivariant homotopy groups corresponds to the reduced G-equivariant connective K-homology groups of X.…”

Section: Introductionmentioning

confidence: 99%

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Induced character in equivariant K-theory and wreath products

Combariza,

Rodríguez,

Velásquez

2019

Preprint

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Let G be a finite group, X be a compact G-space. In this note we study the (Z + × Z/2Z)-graded algebradefined in terms of equivariant K-theory with respect to wreath products as a symmetric algebra. More specifically, let H be another finite group and Y be a compact H-space, we give a decomposition of F q G×H (X × Y ) in terms of F q G (X) and F q H (Y ). For this, we need to study the representation theory of pullbacks of groups. We discuss also some applications of the above result to equivariant connective K-homology. NotationIn this note we denote by S n the symmetric group in n letters. Let G be a finite group, let g, g ′ ∈ G, we say that g and g ′ are conjugated in G (denoted by g ∼ G g ′ ) if there is s ∈ G such that g = sg ′ s −1 . We denote byto the conjugacy class of g in G (or simply by [g] when G is clear from the context). We denote by G * the set of conjugacy classes of G. We denote by C G (g) the centralizer of g in G. Also R(G) will be the complex representation ring of G, with operations given by direct sum and tensor product, and generated as abelian group by the isomorphism classes of irreducible representations of G. The class function ring of G is the set Class(G) = {f : G → C | f is constant in conjugacy classes} with the usual operations.

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Induced character in equivariant K-theory, wreath products and pullback of groups

2022

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Let G be a finite group and let X be a compact G-space. In this note we study the (Z+ × Z/2Z)-graded algebra FqG (X) = ⊕n ≤ 0 qn · KG∫Gn(Xn) ⊗ C, defined in terms of equivariant K-theory with respect to wreath products as a symmetric algebra, we review some properties of FqG (X) proved by Segal and Wang. We prove a Kunneth type formula for this graded algebras, more specifically, let H be another finite group and let Y be a compact H-space, we give a decomposition of FqG × H (X × Y) in terms of FqG (X) and FqH (Y). For this, we need to study the representation theory of pullbacks of groups. We discuss also some applications of the above result to equivariant connective K-homology.

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A configuration space for equivariant connective K-homology

Cited by 4 publications

References 15 publications

A description of the assembly map for the Baum-Connes conjecture with coefficients

A description of the assembly map for the Baum-Connes conjecture with coefficients

Induced character in equivariant K-theory and wreath products

Induced character in equivariant K-theory, wreath products and pullback of groups

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