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Applications of the Homotopy Theory of DG Categories

Student: Poliakova Daria

Supervisor: Christopher Ira Brav

Faculty: Faculty of Mathematics

Educational Programme: Mathematics (Bachelor)

Final Grade: 9

Year of Graduation: 2016

For a topological space X, we define the local systems of complexes - the infinity-category of them and the DG category of them. We conjecture a relation between these two categories. We show that for a path connected space X the complex of chains on based loops is quasiisomorphic to the endomorphism complex of a particular local system and thus it is a DG algebra. We then prove that the DG category of local systems on X is quasiequivalent to the DG category of modules over chains on based loops.

Full text (added June 15, 2016)

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