Abstract
The chapter begins by introducing the notion of a homotopy of DGA maps. Then, an obstruction theory lifting maps and homotopies over a Hirsch extension is established. This obstruction theory is used to show that homotopy is an equivalence relation on maps from a given minimal DGA to another given DGA. From this, one establishes that any two minimal models for a given DGA are isomorphic by an isomorphism making the relevant diagram commute up to homotopy. Also, one shows that a map between minimal DGAs inducing an isomorphism on cohomology is an isomorphism.
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Griffiths, P., Morgan, J. (2013). Homotopy Theory of DGAs. In: Rational Homotopy Theory and Differential Forms. Progress in Mathematics, vol 16. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4614-8468-4_11
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DOI: https://doi.org/10.1007/978-1-4614-8468-4_11
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Publisher Name: Birkhäuser, New York, NY
Print ISBN: 978-1-4614-8467-7
Online ISBN: 978-1-4614-8468-4
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