Abstract
Type-II emphasizing Type-II(B) in Ramond–Ramond Sector has been
analyzed and computed from the Atiyah–Hirzebruch spectral sequence
taking E_i sheets for the concerned values of i = 4=∞ and for
E_n^(p,q) for n=1,2,3; several varieties of K–Theories where a
transitive approach has been shown from the KK–Theory to K–Theory to
String Theory concerning Fredholm modules of Atiyah–Singer Index
Theorem and the Baum–Connes conjecture with respect to the Hilbert–A,
Hilbert–B module and c*-algebras also in the reduced form taking Morita
equivalence and the Kasparov composition product where extended
relations has been provided between the equivalence of noncommutative
geometry and noncommutative topology channelized through Poincaré
Duality, Thom Isomorphism and Todd class.