N-Fold Čech Derived Functors and Generalised Hopf Type Formulas

Donadze, Guram; Inassaridze, Nick; Porter, Timothy

doi:10.1007/s10977-005-3115-5

Cited by 32 publications

(52 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Another application of Theorem 3.5 is to obtain the generalised Hopf type formulas for the cyclic homology of algebras, using the method of n-foldČech derived functors [7,13]. We can think as an initial result in this direction the exact sequence…”

Section: Corollary 37 Let K Contain Q a Be An Algebra Which Is Flmentioning

confidence: 99%

See 1 more Smart Citation

Cyclic homology via derived functors

Donadze¹,

Inassaridze

Ladra

2010

Homology, Homotopy and Applications

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Corollary 37 Let K Contain Q a Be An Algebra Which Is Flmentioning

confidence: 99%

“…Proof. Using the method of n-foldČech derived functors, the proof is similar to that given in [6,7] and is left to the reader. For the sketch of the proof see [14].…”

Section: Corollary 37 Let K Contain Q a Be An Algebra Which Is Flmentioning

confidence: 99%

Cyclic homology via derived functors

Donadze¹,

Inassaridze

Ladra

2010

Homology, Homotopy and Applications

Self Cite

View full text Add to dashboard Cite

show abstract

“…Namely, using the purely algebraic method of n-foldČech derived functors developed in [7,12], we provide higher Hopf type formulas for the equivariant integral group homology (Theorem 12), extending the Hopf formula for the second equivariant homology [11] and recovering the Brown-Ellis higher Hopf formulas [2], when the group actions are trivial.…”

mentioning

confidence: 99%

“…To realize the algebraic proof of higher Hopf formulas and their further generalizations, one of the main tools used in [7] is the theory of crossed n-cubes of groups introduced by Ellis and Steiner [9]. An equivariant analog of the notion of crossed n-cubes takes the following form.…”

mentioning

confidence: 99%

Hopf formulas for equivariant integral homology of groups

Inassaridze¹,

Khmaladze²

2010

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

Abstract. By using purely algebraic methods of n-foldČech derived functors, the higher equivariant integral group homology is investigated from the Hopf formulas point of view.The study of group actions on algebraic objects has many important applications in homotopy theory and K-theory (see for instance [3,10,13,15]). In [11] the first author introduced and studied a natural equivariant version of the classical Eilenberg-Mac Lane (co)homology theory of groups, which can be considered as a part of relative homological algebra. The cohomological characterization of equivariant extensions with operators that are splitting with respect to group actions has motivated the development of this theory, which differs from the (co)homology theory of groups with operators developed in [5,6] motivated by the classification problem of graded categorical groups. Analogues of much of the theory of the classical homological algebra of groups have been obtained in that equivariant setting such as (co)chain and cotriple presentations, the Hopf formula, exact (co)homology sequences, and the Tate cohomology of groups. Moreover, the relationship with the equivariant cohomology of spaces was established, and it was shown that the well known isomorphism of Milnor's K-group K 2 (A) with the second integral homology H 2 (E(A)) of the elementary group E(A) of a unital ring A remains true for arbitrary rings by taking into account the action on E(A) of the Steinberg group St(Z) of the ring Z of integers (see [11, Corollary 24]).As promised we continue the investigation of equivariant homology theory of H. Inassaridze [11]. Namely, using the purely algebraic method of n-foldČech derived functors developed in [7,12], we provide higher Hopf type formulas for the equivariant integral group homology (Theorem 12), extending the Hopf formula for the second equivariant homology [11] and recovering the Brown-Ellis higher Hopf formulas [2], when the group actions are trivial.We set up the following notation. Throughout Γ is a fixed group. G Γ denotes the category of Γ-groups whose objects are groups enriched with a (left) Γ-action and morphisms are Γ-equivariant group homomorphisms, or Γ-homomorphisms for

show abstract

“…, R n ) deve ser conexo não foi incluída no artigo original [BE88], e contraexemplos para o enunciado original foram encontrados por outros autores. Um tal contraexemplo, assim como uma demonstração puramente algébrica desse resultado, pode ser encontrado no artigo de Donadze, Inassaridze e Porter [DIP05].…”

Section: Excisão Teorema De Hurewicz E Fórmulas De Hopfunclassified

Topologia algébrica não-abeliana

Vieira¹

View full text Add to dashboard Cite

N-Fold Čech Derived Functors and Generalised Hopf Type Formulas

Cited by 32 publications

References 33 publications

Cyclic homology via derived functors

Cyclic homology via derived functors

Hopf formulas for equivariant integral homology of groups

Topologia algébrica não-abeliana

Contact Info

Product

Resources

About