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Simplicial homotopy theory SemesterSoSe 2018 Lecturer Matan Prasma Type of course (Veranstaltungsart) Vorlesung Contents Topological spaces were the historical framework in which the 'homotopy theory of spaces' was developed. However, the role of (point-set) topology in homotopy theory is contingent, and there are several ways to model the homotopy theory of spaces without reference to the notion of Topology. One such way is to replace topological spaces by combinatorial objects, called simplicial sets which can be viewed as generalised simplicial complexes. This course will give a detailed account on how to construct the homotopy theory (more precisely, the Quillen model structure) of spaces in the category of simplicial sets, and establish an 'equivalence of homotopy theories' between it and the homotopy theory of topological spaces. Modelling spaces by simplicial sets is popular in the modern literature, and in particular frequently used in Higher Topos Theory and Higher Algebra. The material in this course could thus serve as a prerequisite for a reading of these books. We will follow a book by Goerss-Jardine and lecture notes of Joyal with the same title. Literature see above Recommended previous knowledge Basic knowledge in Category Theory and point-set Topology. Time/Date Fri, 4-6 pm Location M009 Registration
This is a BLOCK COURSE which will run exactly the first 6 weeks of the term. Modules MV, MArGeo, MGAGeo ECTS 6 |