Logarithmic and Tiling Cohomology with Projective Spectrum

Abstract

We give a cohomology of the complement of a free divisor and the computation of the logarithmic cohomology of the complement of a plane curve and for plane curves.The pattern-equivariant and comparing different versions of Tiling cohomology with integer coefficients are shown. The projective spectrum and cyclic cohomology are also shown. The W_n-action on the consective commutators, on the lower central series, an upper bound for the lower central series quotients of a free and graded associative algebra are considered .We also consider the lower central series of a free associative algebra over the integers and finite fields. We study the projective spectrum in Banach algebras and the spectrum of operator –valued entire functions .