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Open/Closed String Topology and Moduli Space Actions via Open/Closed Hochschild Actions
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6
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Open/Closed String Topology and Moduli Space Actions via Open/Closed Hochschild Actions
Інший ID:
2010 Mathematics Subject Classification: 55P48; 81T30; 57R30; 16E40; 55P50
DOI:10.3842/SIGMA.2010.036
DOI:10.3842/SIGMA.2010.036
Посилання:
Open/Closed String Topology and Moduli Space Actions via Open/Closed Hochschild Actions / R.M. Kaufmann // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 21 назв. — англ.
Підтримка:
This paper is a contribution to the Proceedings of the XVIIIth International Colloquium on Integrable Systems and Quantum Symmetries (June 18–20, 2009, Prague, Czech Republic). The full collection is available at http://www.emis.de/journals/SIGMA/ISQS2009.html.
This project was completed in many phases over the last couple of years. We wish to thank the institutes at which we worked on it for their hospitality and support. These are the MPI, IHES where this work was conceived, and the CTQM in Aarhus where many of the final details were fixed. We also wish to thank Bob Penner and Jørgen Andersen for discussions. Special thanks goes to the organizers of the conference ISQS 2009 which provided the forum to present these ideas and prompted me to finish the project and write up the results. We also gratefully acknowledge support from the NSF grant DMS-080588.
Дата:
2010
Переглядів:
491
Завантажень:
259
Анотація:
In this paper we extend our correlation functions to the open/closed case. This gives rise to actions of an open/closed version of the Sullivan PROP as well as an action of the relevant moduli space. There are several unexpected structures and conditions that arise in this extension which are forced upon us by considering the open sector. For string topology type operations, one cannot just consider graphs, but has to take punctures into account and one has to restrict the underlying Frobenius algebras. In the moduli space, one first has to pass to a smaller moduli space which is closed under open/closed duality and then consider covers in order to account for the punctures.
