Variations on Hochschild and Cyclic Cohomology and Spectral Sequences

<p dir="ltr">The purpose of this thesis is to relate some established theory of Hochschild and cyclic cohomology for associative algebras, with some more recent developments of spectral sequences for Hochschild cohomology of differential graded algebras (dgas) and discuss its connection to A∞-algebras. We present a new generalisation of the construction of the spectral sequences of a bicomplex, and use it to construct several new spectral sequences for calculating the cyclic cohomology of a dga. Then we use these spectral sequences to explicitly describe the low dimensional cyclic cohomology, and also prove some technical results about how cyclic and Hochschild cohomology is related in the dga setting. Finally we show how some of these results and the spectral sequences extend naturally to dg-categories.</p>