Category theory provides structure for the mathematical world and is seen everywhere in
modern mathematics. With this book, the author bridges the gap between pure category …

We study higher Hochschild homology evaluated on wedges of circles, viewed as a functor
on the category of free groups. The principal results use coefficients arising from square …

In this short note we show that representation and character varieties of discrete groups can
be viewed as tensor products of suitable functors over the PROP of cocommutative Hopf …

Let G be a reductive affine algebraic group defined over a field k of characteristic zero. We
study the cotangent complex of the derived G–representation scheme DRep G (X) of a …

We study the question for which commutative ring spectra $ A $ the tensor of a simplicial set
$ X $ with $ A $, $ X\otimes A $, is a stable invariant in the sense that it depends only on the …

Tensoring finite pointed simplicial sets X with commutative ring spectra R yields important
homology theories such as (higher) topological Hochschild homology and torus homology …

In a series of papers [35–39], L. Ng introduced and studied a new algebraic invariant of a
link L in R3 represented by a semi-free differential graded (DG) algebra AL. The structure of …

We develop a spectral sequence for the homotopy groups of Loday constructions with
respect to twisted cartesian products in the case where the group involved is discrete. We …

This thesis has four parts. In the first part, we introduce and study representation homology
of topological spaces, which is a higher homological extension of representation varieties of …