Jean-Louis Loday (CNRS and Zinbiel Institute of Mathematics, Strasbourg), Homotopy Transfer Theorem
Schedule
- Feb. 29, 2012, 14:00 - 15:00
- March 2, 2012, 14:00 - 15:00
Abstract
Let (A,d) be a chain complex and (V,d) be a sub-complex that we assume to be a deformation retract of A. If A bears some algebraic structure (like module over an associative algebra, or an algebra structure of some type), then it is not always the case that V is endowed with this very same structure. However, in good cases, there is a notion of ''structure up to homotopy'' which is supported by V. The game consists in unraveling this ''structure up to homotopy'' when given a specific algebraic structure on A. For instance if (A,d) is an associative differential graded algebra, then (V,d) is an A-infinity algebra. We investigate a large class of examples and we show how the methods of rewriting systems help to solve this problem. We explain the relationship with spectral sequences, Koszul duality, Grobner-Shirshov basis, crossed modules and even DNA.
Let (A,d) be a chain complex and (V,d) be a sub-complex that we assume to be a deformation retract of A. If A bears some algebraic structure (like module over an associative algebra, or an algebra structure of some type), then it is not always the case that V is endowed with this very same structure. However, in good cases, there is a notion of ''structure up to homotopy'' which is supported by V. The game consists in unraveling this ''structure up to homotopy'' when given a specific algebraic structure on A. For instance if (A,d) is an associative differential graded algebra, then (V,d) is an A-infinity algebra. We investigate a large class of examples and we show how the methods of rewriting systems help to solve this problem. We explain the relationship with spectral sequences, Koszul duality, Grobner-Shirshov basis, crossed modules and even DNA.