Which homotopy algebras come from transfer?
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- by Martin Markl and Christopher L. Rogers PDF
- Proc. Amer. Math. Soc. 150 (2022), 975-990 Request permission
Abstract:
We characterize $A_\infty$-structures that are equivalent to a given transferred structure over a chain homotopy equivalence or a quasi-isomorphism, answering a question posed by D. Sullivan. Along the way, we present an obstruction theory for weak \text{$A_\infty$-morphisms} over an arbitrary commutative ring. We then generalize our results to $\mathcal {P}_\infty$-structures over a field of characteristic zero, for any quadratic Koszul operad $\mathcal {P}$.References
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Additional Information
- Martin Markl
- Affiliation: The Czech Academy of Sciences, Institute of Mathematics, Žitná 25, 115 67 Prague, Czech Republic
- MR Author ID: 120045
- ORCID: 0000-0003-4611-8226
- Email: markl@math.cas.cz
- Christopher L. Rogers
- Affiliation: Department of Mathematics and Statistics, University of Nevada, Reno,1664 N. Virginia Street, Reno, Nevada 89557-0084
- MR Author ID: 888087
- Email: chrisrogers@unr.edu, chris.rogers.math@gmail.com
- Received by editor(s): June 17, 2020
- Received by editor(s) in revised form: February 17, 2021, May 11, 2021, and June 10, 2021
- Published electronically: December 17, 2021
- Additional Notes: This material is based upon work supported by the National Science Foundation under Grant No. DMS-1440140 while the authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Spring 2020 semester. The first author was also supported by grant GA ČR 18-07776S, Praemium Academiæ and RVO: 67985840. The second author was also supported by a grant from the Simons Foundation/SFARI (585631,CR)
- Communicated by: Julie Bergner
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 975-990
- MSC (2020): Primary 13D99, 55S20
- DOI: https://doi.org/10.1090/proc/15710
- MathSciNet review: 4375697