Lecture 1:
- Hochschild and coHochschild complex generalized to functors [W, Def 1.1]
- PROPS. Examples: A_\infty, Com, Frobenius (brief, see eg [WW, Sec 3]
- Definition of the natural and formal operations on the Hochschild complex
- Explicit description of the formal operations [W, Thm 2.1] (with proof if time permits)
- Relationship between the formal and natural operations [W, Thm 2.9]
- Example: the cap product [W, Sec 2.3].
Lecture 2:
- Practical construction of formal operations via action on the Hochschild complex of representable functors [WW, Thm 5.11]
- Example: open field theories (Costello/Konstevich-Soibelman's theorem) [WW, Sec 6.1]
- Example: Frobenius algebras (Tradler-Zeinalian) [WW, Sec 6.5]
- Computations of all the formal operations in the case open field theories [W, Sec 3.1]
- Application to string topology [W, Sec 4]
References:
[W] Wahl, "Universal operations in Hochschild homology", arXiv:1212.6498
[WW] Wahl and Westerland, "Hochschild homology of structured algebras", arXiv:1110.0651