Antiperfect morse stratification

作者：Ho Nan Kuo^*; Liu Chiu Chu Melissa

来源：Selecta Mathematica, New Series, 2011, 17(2): 505-532.

DOI：10.1007/s00029-010-0042-y

• Morse theory
• Moduli space

For an equivariant Morse stratification that contains a unique open stratum, we introduce the notion of equivariant antiperfection, which means the difference of the equivariant Morse series and the equivariant Poincar, series achieves the maximal possible value (instead of the minimal possible value 0 in the equivariantly perfect case). We also introduce a weaker condition of local equivariant antiperfection. We prove that the Morse stratification of the Yang-Mills functional on the space of connections on a principal G-bundle over a connected, closed, nonorientable surface I pound is locally equivariantly Q-antiperfect when G = U(2), SU(2), U(3), SU(3); we propose that the Morse stratification is actually equivariantly Q-antiperfect in these cases. Our proposal yields formulas of Poincare, series P(t)(G) (Hom (pi(1)(Sigma), G); Q) when G = U(2), SU(2), U(3), SU(3). Our U(2), SU(2) formulas agree with formulas proved by T. Baird, who also verified our conjectural U(3) formula.

• 出版日期2011-6
• 单位清华大学