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

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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 languageEnglish
Pages (from-to)465-482
Number of pages18
JournalInternational Journal of Mathematics
Volume22
Issue number4
DOIs
Publication statusPublished - Apr 2011

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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