Abstract
We provide a general method for nding all natural operations on the Hochschild complex of E-algebras, where E is any algebraic structure encoded in a PROP with multiplication, as for example the PROP of Frobenius, commutative or A1-algebras. We show that the chain complex of all such natural operations is approximated by a certain chain complex of formal operations, for which we provide an explicit model that we can calculate in a number of cases. When E encodes the structure of open topological conformal eld theories, we identify this last chain complex, up quasi-isomorphism, with the moduli space of Riemann surfaces with boundaries, thus establishing that the operations constructed by Costello and Kontsevich-Soibelman via dierent methods identify with all formal operations. When E encodes open topological quantum eld theories (or symmetric Frobenius algebras) our chain complex identies with Sullivan diagrams, thus showing that operations constructed by Tradler-
Zeinalian, again by dierent methods, account for all formal operations. As an illustration of the last result we exhibit two innite families of non-trivial operations and use these to produce non-trivial higher string topology operations, which had so far been elusive.
Zeinalian, again by dierent methods, account for all formal operations. As an illustration of the last result we exhibit two innite families of non-trivial operations and use these to produce non-trivial higher string topology operations, which had so far been elusive.
| Originalsprog | Engelsk |
|---|---|
| Tidsskrift | Journal fuer die Reine und Angewandte Mathematik |
| Vol/bind | 2016 |
| Udgave nummer | 720 |
| Sider (fra-til) | 81-127 |
| ISSN | 0075-4102 |
| DOI | |
| Status | Udgivet - nov. 2016 |