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The cyclic open-closed map, u-connections and R-matrices

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The cyclic open-closed map, u-connections and R-matrices. / Hugtenburg, Kai.
In: Selecta Mathematica, Vol. 30, 29, 27.02.2024.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Hugtenburg, K 2024, 'The cyclic open-closed map, u-connections and R-matrices', Selecta Mathematica, vol. 30, 29. https://doi.org/10.1007/s00029-024-00925-7

APA

Hugtenburg, K. (2024). The cyclic open-closed map, u-connections and R-matrices. Selecta Mathematica, 30, Article 29. https://doi.org/10.1007/s00029-024-00925-7

Vancouver

Hugtenburg K. The cyclic open-closed map, u-connections and R-matrices. Selecta Mathematica. 2024 Feb 27;30:29. doi: 10.1007/s00029-024-00925-7

Author

Hugtenburg, Kai. / The cyclic open-closed map, u-connections and R-matrices. In: Selecta Mathematica. 2024 ; Vol. 30.

Bibtex

@article{5b5adf8fc2bb418288922304c29e32d3,
title = "The cyclic open-closed map, u-connections and R-matrices",
abstract = "This paper considers the (negative) cyclic open-closed map OC, which maps the cyclic homology of the Fukaya category of a symplectic manifold to its S1-equivariant quantum cohomology. We prove (under simplifying technical hypotheses) that this map respects the respective natural connections in the direction of the equivariant parameter. In the monotone setting this allows us to conclude that OC intertwines the decomposition of the Fukaya category by eigenvalues of quantum cup product with the first Chern class, with the Hukuhara-Levelt-Turrittin decomposition of the quantum cohomology. We also explain how our results relate to the Givental-Teleman classification of semisimple cohomological field theories: in particular, how the R-matrix is related to OC in the semisimple case; we also consider the non-semisimple case.",
author = "Kai Hugtenburg",
year = "2024",
month = feb,
day = "27",
doi = "10.1007/s00029-024-00925-7",
language = "English",
volume = "30",
journal = "Selecta Mathematica",
issn = "1420-9020",
publisher = "Springer",

}

RIS

TY - JOUR

T1 - The cyclic open-closed map, u-connections and R-matrices

AU - Hugtenburg, Kai

PY - 2024/2/27

Y1 - 2024/2/27

N2 - This paper considers the (negative) cyclic open-closed map OC, which maps the cyclic homology of the Fukaya category of a symplectic manifold to its S1-equivariant quantum cohomology. We prove (under simplifying technical hypotheses) that this map respects the respective natural connections in the direction of the equivariant parameter. In the monotone setting this allows us to conclude that OC intertwines the decomposition of the Fukaya category by eigenvalues of quantum cup product with the first Chern class, with the Hukuhara-Levelt-Turrittin decomposition of the quantum cohomology. We also explain how our results relate to the Givental-Teleman classification of semisimple cohomological field theories: in particular, how the R-matrix is related to OC in the semisimple case; we also consider the non-semisimple case.

AB - This paper considers the (negative) cyclic open-closed map OC, which maps the cyclic homology of the Fukaya category of a symplectic manifold to its S1-equivariant quantum cohomology. We prove (under simplifying technical hypotheses) that this map respects the respective natural connections in the direction of the equivariant parameter. In the monotone setting this allows us to conclude that OC intertwines the decomposition of the Fukaya category by eigenvalues of quantum cup product with the first Chern class, with the Hukuhara-Levelt-Turrittin decomposition of the quantum cohomology. We also explain how our results relate to the Givental-Teleman classification of semisimple cohomological field theories: in particular, how the R-matrix is related to OC in the semisimple case; we also consider the non-semisimple case.

U2 - 10.1007/s00029-024-00925-7

DO - 10.1007/s00029-024-00925-7

M3 - Journal article

VL - 30

JO - Selecta Mathematica

JF - Selecta Mathematica

SN - 1420-9020

M1 - 29

ER -