### 抄録

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.

元の言語 | 英語 |
---|---|

ページ（範囲） | 465-482 |

ページ数 | 18 |

ジャーナル | International Journal of Mathematics |

巻 | 22 |

発行部数 | 4 |

DOI | |

出版物ステータス | 出版済み - 4 1 2011 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### これを引用

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

研究成果: ジャーナルへの寄稿 › 記事

*International Journal of Mathematics*, 巻. 22, 番号 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 -