On the structure of open equivariant topological conformal field theories
DOI:
https://doi.org/10.7146/math.scand.a-122371Abstract
A classification of open equivariant topological conformal field theories in terms of Calabi-Yau $A_\infty $-categories endowed with a group action is presented.
References
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Fernàndez-València, R., On the structure of unoriented topological conformal field theories, Geom. Dedicata 189 (2017), 113–138. https://doi.org/10.1007/s10711-017-0220-6
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Husemoller, D., Fibre bundles, third ed., Graduate Texts in Mathematics, vol. 20, Springer-Verlag, New York, 1994. https://doi.org/10.1007/978-1-4757-2261-1
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Markl, M., Shnider, S., and Stasheff, J., Operads in algebra, topology and physics, Mathematical Surveys and Monographs, vol. 96, American Mathematical Society, Providence, RI, 2002. https://doi.org/10.1090/surv/096
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Moore, G. W. and Segal, G., D-branes and K-theory in $2$D topological field theory, 2006, eprint arXiv:hep-th/0609042.
Turaev, V., Homotopy field theory in dimension $3$ and crossed group-categories, eprint arXiv:math/0005291 [math.GT], 2000.
Costello, K. J., The $A_\infty $ operad and the moduli space of curves, eprint arXiv:math/0402015v2 [math.AG], 2004.
Costello, K. J., A dual version of the ribbon graph decomposition of moduli space, Geom. Topol. 11 (2007), 1637–1652. https://doi.org/10.2140/gt.2007.11.1637
Costello, K. J., Topological conformal field theories and Calabi-Yau categories, Adv. Math. 210 (2007), no. 1, 165–214. https://doi.org/10.1016/j.aim.2006.06.004
Fernàndez-València, R., On the structure of unoriented topological conformal field theories, Geom. Dedicata 189 (2017), 113–138. https://doi.org/10.1007/s10711-017-0220-6
Giansiracusa, J. H., Moduli spaces and modular operads, Morfismos 17 (2013), no. 2, 101–125.
Husemoller, D., Fibre bundles, third ed., Graduate Texts in Mathematics, vol. 20, Springer-Verlag, New York, 1994. https://doi.org/10.1007/978-1-4757-2261-1
Lefèvre-Hasegawa, K., Sur les $A_\infty $-catégories, Ph.D. thesis, Université Paris 7 - Denis Diderot, 2003, eprint arXiv:math/0310337.
Mac Lane, S., Categorical algebra, Bull. Amer. Math. Soc. 71 (1965), 40–106. https://doi.org/10.1090/S0002-9904-1965-11234-4
Markl, M., Shnider, S., and Stasheff, J., Operads in algebra, topology and physics, Mathematical Surveys and Monographs, vol. 96, American Mathematical Society, Providence, RI, 2002. https://doi.org/10.1090/surv/096
Moore, G., Some comments on branes, $G$-flux, and $K$-theory, in “Strings 2000. Proceedings of the International Superstrings Conference (Ann Arbor, MI)”, vol. 16, 2001, pp. 936–944. https://doi.org/10.1142/S0217751X01004010
Moore, G. W. and Segal, G., D-branes and K-theory in $2$D topological field theory, 2006, eprint arXiv:hep-th/0609042.
Turaev, V., Homotopy field theory in dimension $3$ and crossed group-categories, eprint arXiv:math/0005291 [math.GT], 2000.
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Published
2021-02-17
How to Cite
Fernàndez-València, R. (2021). On the structure of open equivariant topological conformal field theories. MATHEMATICA SCANDINAVICA, 127(1), 63–78. https://doi.org/10.7146/math.scand.a-122371
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