• Sudarshan Kumar

The main object of this paper is the construction of the Serre spectral sequence by means of twisted tensor products. The basic tool in this development, which is completed in section 32, is Brown’s theorem, which gives a natural equivalence between CN(F Xτ B) and CN(B) ⊗t CN(F) on the category of twisted Cartesian products, where t is a twisting cochain determined by the twisting function τ. In order to define twisting cochains, the theory of cup, Pontryagin, and cap products is developed in [3]. Of course, the definition of these products depends on the Eilenberg-Zilber theorem, and this is proven in ref [4]. The proofs of bothe Brown’s theorem and the Eilenberg-Zilber theorem rely on the method of acyclic models, which is described in ref [5] . The models for Brown’s theorem are defined in terms of functions which assign to a (reduced) simplicial set K a simplicial group G(K) and a PTCP G(K) Xτ K such that T(E(τ)) is contractible. G(K) is called a loop group of K. G(K) and G(K) Xτ K are defined in [6] . In ref [7], it is shown that G and W ̅ are adjoint functions, the suspension E(K) of a complex K is defined, and miscellaneous results about the functions G, W ̅ and E are obtained.

STUDY OF THE LOOP GROUPS ACYCLIC MODELS, AND TWISTED TENSOR PRODUCTS

"STUDY OF THE LOOP GROUPS ACYCLIC MODELS, AND TWISTED TENSOR PRODUCTS", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.5, Issue 4, page no.1043-1051, April-2018, Available :http://www.jetir.org/papers/JETIR1804395.pdf

"STUDY OF THE LOOP GROUPS ACYCLIC MODELS, AND TWISTED TENSOR PRODUCTS", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.5, Issue 4, page no. pp1043-1051, April-2018, Available at : http://www.jetir.org/papers/JETIR1804395.pdf