Kernel Functions, Analytic Torsion, and Moduli Spaces (Memoirs of the AMS) (Memoirs of the American Mathematical Society) - Softcover

American Mathematical Society

 
9780821825501: Kernel Functions, Analytic Torsion, and Moduli Spaces (Memoirs of the AMS) (Memoirs of the American Mathematical Society)

Synopsis

This work investigates analytic torsion on the moduli space of degree zero stable bundles on a compact Reimann surface. Zeta-function regularization and perturbation-curvature formulas for torsion are developed using a modified resolvent-Szego kernel. The author discusses the bosonization formulas of mathematical physics. Riemann vanishing theorems for torsion, and analytic properties (insertion-residue formulas and heat equations) for the nonabelian theta function and Szego
kernel. In addition, he provides background material on bundle-moduli spaces, Quillen metrics, and theta functions.

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