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Cartan's constructions and the twisted Eilenberg–Zilber theorem
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Víctor Álvarez
Veröffentlicht/Copyright:
19. März 2010
Abstract
Let 𝐺 × τ 𝐺′ be the principal twisted Cartesian product with fibre 𝐺, base 𝐺 and twisting function 
where 𝐺 and 𝐺′ are simplicial groups as well as 𝐺 × τ 𝐺′; and 𝐶𝑁(𝐺) ⊗𝑡 𝐶𝑁 (𝐺′) be the twisted tensor product associated to 𝐶𝑁 (𝐺 × τ 𝐺′) by the twisted Eilenberg–Zilber theorem. Here we prove that the pair 𝐶𝑁(𝐺) ⊗𝑡 𝐶𝑁(𝐺′), μ) is a multiplicative Cartan's construction where μ is the standard product on 𝐶𝑁(𝐺) ⊗ 𝐶𝑁(𝐺′). Furthermore, assuming that a contraction from 𝐶𝑁(𝐺′) to 𝐻𝐺′ exists and using the techniques from homological perturbation theory, we extend the former result to other “twisted” tensor products of the form 𝐶𝑁(𝐺) ⊗ 𝐻𝐺′.
Keywords.: Simplicial groups; twisted Cartesian product; Eilenberg–Zilber theorem; Cartan's construction; contraction; homological perturbation lemma
Received: 2008-12-29
Published Online: 2010-03-19
Published in Print: 2010-March
© de Gruyter 2010
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Artikel in diesem Heft
- A finite dimensional 𝐴∞ algebra example
- Cartan's constructions and the twisted Eilenberg–Zilber theorem
- Higher order track categories and the algebra of higher order cohomology operations
- A case study of 𝐴∞-structure
- Props in model categories and homotopy invariance of structures
- On the construction of 𝐴∞-structures
- A twisted tale of cochains and connections
Schlagwörter für diesen Artikel
Simplicial groups;
twisted Cartesian product;
Eilenberg–Zilber theorem;
Cartan's construction;
contraction;
homological perturbation lemma
Artikel in diesem Heft
- A finite dimensional 𝐴∞ algebra example
- Cartan's constructions and the twisted Eilenberg–Zilber theorem
- Higher order track categories and the algebra of higher order cohomology operations
- A case study of 𝐴∞-structure
- Props in model categories and homotopy invariance of structures
- On the construction of 𝐴∞-structures
- A twisted tale of cochains and connections
