### Abstract

We give an explicit presentation of the SO(N) and Sp(N) free energy of lens spaces and show that the genus g terms of it are analytic in a neighborhood at zero, where we can choose the neighborhood independently of g. Moreover, we prove that for any rational homology three-sphere M and any g, the genus g terms of SO(N) and Sp(N) free energy of M agree up to sign. We also observe new weight systems related to the free energy.

Original language | English |
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Pages (from-to) | 465-482 |

Number of pages | 18 |

Journal | International Journal of Mathematics |

Volume | 22 |

Issue number | 4 |

DOIs | |

Publication status | Published - Apr 1 2011 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

**On the SO(N) and Sp(N) free energy of a rational homology three-sphere.** / Takata, Toshie.

Research output: Contribution to journal › Article

*International Journal of Mathematics*, vol. 22, no. 4, pp. 465-482. https://doi.org/10.1142/S0129167X11006866

}

TY - JOUR

T1 - On the SO(N) and Sp(N) free energy of a rational homology three-sphere

AU - Takata, Toshie

PY - 2011/4/1

Y1 - 2011/4/1

N2 - We give an explicit presentation of the SO(N) and Sp(N) free energy of lens spaces and show that the genus g terms of it are analytic in a neighborhood at zero, where we can choose the neighborhood independently of g. Moreover, we prove that for any rational homology three-sphere M and any g, the genus g terms of SO(N) and Sp(N) free energy of M agree up to sign. We also observe new weight systems related to the free energy.

AB - We give an explicit presentation of the SO(N) and Sp(N) free energy of lens spaces and show that the genus g terms of it are analytic in a neighborhood at zero, where we can choose the neighborhood independently of g. Moreover, we prove that for any rational homology three-sphere M and any g, the genus g terms of SO(N) and Sp(N) free energy of M agree up to sign. We also observe new weight systems related to the free energy.

UR - http://www.scopus.com/inward/record.url?scp=79955610073&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79955610073&partnerID=8YFLogxK

U2 - 10.1142/S0129167X11006866

DO - 10.1142/S0129167X11006866

M3 - Article

AN - SCOPUS:79955610073

VL - 22

SP - 465

EP - 482

JO - International Journal of Mathematics

JF - International Journal of Mathematics

SN - 0129-167X

IS - 4

ER -