The Yang-mills Heat Flow on the Moduli Space of Framed Bundles on a Surface
نویسنده
چکیده
We study the analog of the Yang-Mills heat flow on the moduli space of framed bundles on a cut surface. Existence and convergence of the heat flow give a stratification of Morse type invariant under the action of the loop group. We use the stratification to prove versions of Kähler quantization commutes with reduction and Kirwan surjectivity.
منابع مشابه
A Duality for Yang-Mills Moduli Spaces on Noncommutative Manifolds
Studied are the moduli spaces of Yang-Mills connections on finitely generated projective modules associated with noncommutative flows. It is actually shown that they are homeomorphic to those on dual modules associated with dual noncommutative flows. Moreover the method is also applicable to the case of noncommutative multi-flows. As an important application, computed are the the moduli spaces ...
متن کاملModuli Space of Self-Dual Gauge Fields, Holomorphic Bundles and Cohomology Sets
We discuss the twistor correspondence between complex vector bundles over a self-dual four-dimensional manifold and holomorphic bundles over its twistor space and describe the moduli space of self-dual Yang-Mills fields in terms of Čech and Dolbeault cohomology sets. The cohomological description provides the geometric interpretation of symmetries of the self-dual Yang-Mills equations.
متن کاملModuli Spaces of Bundles over Riemann Surfaces and the Yang–Mills Stratification Revisited
Refinements of the Yang–Mills stratifications of spaces of connections over a compact Riemann surface Σ are investigated. The motivation for this study is the search for a complete set of relations between the standard generators for the cohomology of the moduli spaces M(n, d) of stable holomorphic bundles of rank n and degree d when n and d are coprime and n > 2. The moduli space M(n, d) of se...
متن کاملYang-Mills Theory for Noncommutative Flows Addendum
This supplementary manuscript is to describe an important nontrivial example, which appears in the matrix model of type IIB in the super string theory in order to apply a new duality for the moduli spaces of YangMills connections on noncommutative vector bundles. Actually, the moduli space of the instanton bundle over noncommutative Euclidean 4-spaces with respect to the canonical action of spa...
متن کاملYang-mills Theory and Tamagawa Numbers: the Fascination of Unexpected Links in Mathematics
Atiyah and Bott used equivariant Morse theory applied to the Yang–Mills functional to calculate the Betti numbers of moduli spaces of vector bundles over a Riemann surface, rederiving inductive formulae obtained from an arithmetic approach which involved the Tamagawa number of SLn. This article attempts to survey and extend our understanding of this link between Yang–Mills theory and Tamagawa n...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008