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000220241 001__ 220241 000220241 005__ 20190509132558.0 000220241 0247_ $$2doi$$a10.5075/epfl-thesis-7127 000220241 02470 $$2urn$$aurn:nbn:ch:bel-epfl-thesis7127-4 000220241 02471 $$2nebis$$a10687447 000220241 037__ $$aTHESIS 000220241 041__ $$aeng 000220241 088__ $$a7127 000220241 245__ $$aCellular Homotopy Excision 000220241 269__ $$a2016 000220241 260__ $$bEPFL$$c2016$$aLausanne 000220241 300__ $$a288 000220241 336__ $$aTheses 000220241 502__ $$aProf. Marc Troyanov (président) ; Prof. Kathryn Hess Bellwald, Dr Jérôme Scherer (directeurs) ; Prof. Tamás Hausel, Prof. Wojciech Chachólski, Prof. Emmanuel Dror Farjoun (rapporteurs) 000220241 520__ $$aThere 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 long exact sequence in homotopy), while homology groups are compatible with homotopy pushouts (every homotopy pushout gives rise to a long exact sequence in homology). This last statement is sometimes referred to as the Mayer-Vietoris or excision axiom. The classical Blakers-Massey theorem (or homotopy excision theorem) asks to what extent the excision property for homotopy pushouts remains true if we replace homology groups by homotopy groups and gives a range in which the excision property holds. It does so by estimating the connectivity of a certain comparison map, which is a rather crude measure, as it is just a single number. Since connectivity is a special case of a cellular inequality, the hope is that there is a stronger statement hidden behind the connectivity result in terms of such inequalities. This process of generalising the homotopy excision theorem has been initiated by Chachólski in the 90s, where he proved a more general version for homotopy pushout squares. The caveat was that one had to suspend the comparison map in question first and the goal of our project -- which we obtained -- was to lose this suspension and then move on to cubical diagrams, rather than squares. To do so, there are a few basic ingredients that are necessary. We first talk about our abstract approach to derived functors, then construct left Bousfield localisations of combinatorial model categories and finally, generalise the foundational concepts in the theory of closed classes to non-connected spaces. 000220241 6531_ $$aHomotopy excision 000220241 6531_ $$aBousfield localisation 000220241 6531_ $$aBousfield classes 000220241 6531_ $$aCellular classes 000220241 6531_ $$aClosed classes 000220241 6531_ $$aDiagrams of spaces 000220241 6531_ $$aDerived functors 000220241 700__ $$0245810$$g216064$$aWerndli, Kay Remo 000220241 720_2 $$aHess Bellwald, Kathryn$$edir.$$g105396$$0240499 000220241 720_2 $$aScherer, Jérôme$$edir.$$g144617$$0243126 000220241 8564_ $$uhttps://infoscience.epfl.ch/record/220241/files/EPFL_TH7127.pdf$$zn/a$$s6449136$$yn/a 000220241 909C0 $$xU10968$$0252139$$pUPHESS 000220241 909CO $$pthesis$$pthesis-bn2018$$pDOI$$ooai:infoscience.tind.io:220241$$qDOI2$$qGLOBAL_SET$$pSV 000220241 917Z8 $$x108898 000220241 917Z8 $$x108898 000220241 917Z8 $$x108898 000220241 917Z8 $$x108898 000220241 918__ $$dEDMA$$cMATHGEOM$$aSB 000220241 919__ $$aGR-HE 000220241 920__ $$b2016$$a2016-8-12 000220241 970__ $$a7127/THESES 000220241 973__ $$sPUBLISHED$$aEPFL 000220241 980__ $$aTHESIS