In this monograph we give an exposition of some recent development in homotopy theory. It
relates to advances in periodicity in homotopy localization and in cellular spaces. The notion …

Let A be a pointed and connected simplicial set. The aim of this thesis is to study the
relationship between Bousfield's localization functor $ P\sb {A} $ and Dror Farjoun's co …

We show that homotopy pullbacks of sheaves of simplicial sets over a Grothendieck
topology distribute over homotopy colimits; this generalizes a result of Puppe about …

Motivated by applications in Topological Data Analysis, we consider decompositions of a
simplicial complex induced by a cover of its vertices. We study how the homotopy type of …

A PPPPPPPq X PPPPPPPq Page 1 A GENERALIZATION OF THE TRIAD THEOREM OF
BLAKERS-MASSEY WOJCIECH CHACHOLSKI 1. Introduction The purpose of this paper is to …

The aim of this paper is twofold. On the one hand, we show that the kernel $\overline {C (A)}
$ of the Bousfield periodization functor $ P_A $ is cellularly generated by a space $ B $, ie …

We show that if $ K $ is a nilpotent finite complex, then $\Omega K $ can be built from
spheres using fibrations and homotopy (inverse) limits. This is applied to show that if …

The way spaces are often studied in homotopy theory is by decomposing and approximating
them using simpler and possibly better understood pieces. This is typically done in two …

This thesis is a compilation of results that can be framed within the field of applied topology.
The starting point of our study is objects presenting a possibly complex intrinsic geometry …

There is a classical" duality" between homotopy and homology groups in that homotopy
groups are compatible with homotopy pullbacks (every homotopy pullback gives rise to a …