منابع مشابه
Twisted bundles and twisted K-theory
Many papers have been devoted recently to twisted K-theory as originally defined in [15] and [29]. See for instance the references [2], [23] and the very accessible paper [30]. We offer here a more direct approach based on the notion of “twisted vector bundles”. This is not an entirely new idea, since we find it in [4], [6], [7], [8] and [9] for instance, under different names and from various ...
متن کاملModuli of Higgs Bundles
2 Local symplectic, complex and Kähler geometry: a quick review 10 2.1 Quotients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 Symplectic manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3 Symplectic quotients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4 Complex manifolds . . . . . . . . . . . . . . ....
متن کاملIntroduction to Higgs Bundles
H(X,C) = H(X)⊕H(X) = H(X,OX)⊕H(X,ΩX). Therefore, homomorphisms π1(X) → C are the same as an element of H(X,OX), i.e. a holomorphic line bundle of degree 0, and an element of H(X,ΩX), i.e. a holomorphic 1-form. In these notes, we describe an analogous correspondence for the case of represenations into a nonabelian Lie Group G, focusing in particular on the case G = GL(n,C) [5]. Theorems are give...
متن کاملHiggs Bundles and Four Manifolds
It is known that the Seiberg-Witten invariants, derived from supersymmetric Yang-Mill theories in four-dimensions, do not distinguish smooth structure of certain non-simply-connected four manifolds. We propose generalizations of Donaldson-Witten and Vafa-Witten theories on a Kähler manifold based on Higgs Bundles. We showed, in particular, that the partition function of our generalized Vafa-Wit...
متن کاملHiggs Bundles and Holomorphic Forms
For a complex manifold X which has a holomorphic form ̟ of odd degree k, we endow E = ⊕ p≥a Λ (p,0)(X) with a Higgs bundle structure θ given by θ(Z)(φ) := {i(Z)̟} ∧ φ. The properties such as curvature and stability of these and other Higgs bundles are examined. We prove (Theorem 2, section 2, for k > 1) E and additional classes of Higgs subbundles of E do not admit Higgs-Hermitian-Yang-Mills metr...
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ژورنال
عنوان ژورنال: Bulletin des Sciences Mathématiques
سال: 2018
ISSN: 0007-4497
DOI: 10.1016/j.bulsci.2018.03.003