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Author Ho, Nan-Kuo ♦ Liu, Chiu-Chu Melissa
Source arXiv.org
Content type Text
File Format PDF
Date of Submission 2008-08-28
Language English
Subject Domain (in DDC) Natural sciences & mathematics ♦ Mathematics
Subject Keyword Mathematics - Symplectic Geometry ♦ Mathematics - Differential Geometry ♦ 14D20 ♦ 53C07 ♦ math
Abstract For an equivariant Morse stratification which contains a unique open stratum, we introduce the notion of equivariant antiperfection, which means the difference of the equivariant Morse series and the equivariant Poincare 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 U(n)-bundle over a connected, closed, nonorientable surface is locally equivariantly Q-antiperfect when the rank n=2,3; we propose that it is actually equivariantly Q-antiperfect when n=2,3. Our proposal yields formulas of G-equivariant Poincare series of the representation variety of flat G-connections for the nonorientable surface where G=U(2), SU(2), U(3), SU(3). Our rank 2 formulas agree with formulas proved by T. Baird in arXiv:0806.1975. Baird verified our conjectural rank 3 formulas when the nonorientable surface is the real projective plane or the Klein bottle (arXiv:0901.1604); he proved our conjectural U(3) formula for any closed nonorientable surfaces by establishing equivariant Q-antiperfection in this case (arXiv:0902.4581).
Description Reference: Selecta Math. (N.S.) 17 (2011), no.2, 505-532
Educational Use Research
Learning Resource Type Article
Page Count 24


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