TY - JOUR
T1 - On the SO(N) and Sp(N) free energy of a rational homology three-sphere
AU - Takata, Toshie
PY - 2011/4
Y1 - 2011/4
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.
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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 -