The master equation package up to homotopy


Dennis Sullivan



Thursday, February 7, 2008

Talk at 4:30 p.m. in Room 4-370

Tea from 4:00 - 4:30 p.m. in Room 2-290
Refreshments afterwards, in Room 2-290


Abstract:   Often systems of moduli spaces that occur in geometry and/or physics have the following special feature. The frontier of one component in the system can be decomposed or factored in terms of other components in the system. This picture creates a differential graded free algebra. The actual moduli spaces can be construed as a dga map of this free dga into a dga described more elementarily in algebraic topology. This map up to homotopy is an invariant of the original situation. The algebraic formalism general enough to carry out this discussion also applies to the classification up to homotopy of general algebraic structures like bialgebras. Considering the top canonical classes of the moduli spaces frequently relates the first discussion to the second. Examples under study include gauge theory on 4 manifolds, 3 manifold invariants, string topology and J-holomorphic curves.


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Posted: January 31, 2008    URL: