ALGEBRA BUNDLES WHOSE m-DIMENSIONAL COHOMOLOGY MODULES ARE ZERO
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Let§ be an algebra bundle and Ƞ be a §-bimodule bundle over a compact Hausdorff space X. Here we prove that the m-dimensional cohomology module Hm(§, Ƞ)is isomorphic to Hm−1(§, ˜ C(§, Ƞ)), where ˜ C(§, Ƞ) is a § bimodule bundle. If we denote Km(F),m = 1, 2, 3, ..., the class of all algebra bundles whose m-dimensional cohomology modules are all zero then it is shown that K1(F) is strictly contained in K2(F) and K2(F) is strictly contained in K3(F). Further we show that if an algebra bundle § is nilpotent then it does not belong to K3(F).
Abstract
Let§ be an algebra bundle and Ƞ be a §-bimodule bundle over a compact Hausdorff space X. Here we prove that the m-dimensional cohomology module Hm(§, Ƞ)is isomorphic to Hm−1(§, ˜ C(§, Ƞ)), where ˜ C(§, Ƞ) is a § bimodule bundle. If we denote Km(F),m = 1, 2, 3, ..., the class of all algebra bundles whose m-dimensional cohomology modules are all zero then it is shown that K1(F) is strictly contained in K2(F) and K2(F) is strictly contained in K3(F). Further we show that if an algebra bundle § is nilpotent then it does not belong to K3(F).
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