Atiyah class
WebMay 2, 2012 · Metrics We provide generalizations of the notions of Atiyah class and Kodaira-Spencer map to the case of framed sheaves. Moreover, we construct closed two-forms on the moduli spaces of framed sheaves on surfaces. As an application, we define a symplectic structure on the moduli spaces of framed sheaves on some birationally ruled … WebApr 1, 2015 · The class is called the Atiyah class of the dg-vector bundle relative to the dg-Lie algebroid . The Atiyah class of a dg-manifold, which is the obstruction to the existence of connections compatible with the differential, was first investigated by Shoikhet [11] in relation with Kontsevich's formality theorem and Duflo formula.
Atiyah class
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WebJul 27, 2024 · University of Tsukuba Abstract This is a review of Atiyah classes of strongly homotopy Lie pairs by Chen, Zhuo; Lang, Honglei; Xiang, Maosong Content uploaded by Hirokazu Nishimura Author... WebJan 1, 2024 · In this section, we introduce the two notions of Atiyah class that we intend to relate in Section 5 in the case of matched pairs of Lie algebroids. The first is the Atiyah …
WebOct 9, 2008 · We develop a formalism involving Atiyah classes of sheaves on a smooth manifold, Hochschild chain and cochain complexes. As an application we prove a version of the Riemann–Roch theorem. The Atiyah class, Hochschild cohomology and the Riemann–Roch theorem - Markarian - 2009 - Journal of the London Mathematical … WebLet X be a complex manifold and $TX$ its tangent bundle. The Atiyah class $\alpha(E)\in \text{Ext}^1(E\otimes TX, E)$ for a vector bundle $E$ is defined to be the ...
WebDec 4, 2007 · Recently, L. Rozansky and E. Witten associated to any hyper-Kähler manifold X a system of ’weights‘ (numbers, one for each trivalent graph) and used them to construct invariants of topological 3-manifolds. WebAtiyah–Jones conjecture it would now suffice to show that the maps tk in-duce isomorphism in homology and homotopy through a range. In 1993, Boyer, Hurtubise, Milgram and Mann [BHMM] proved that the Atiyah–Jones conjecture holds for the sphere S4 and in 1995, Hurtubise and Mann [HM] proved that the conjecture is true for ruled surfaces.
WebMay 10, 2010 · Abstract. We construct the Atiyah classes of holomorphic vector bundles using (1, 0)-connections and developing a Chern-Weil type theory, allowing us to effectively compare Chern and Atiyah forms ...
prayer for protection for family and friendsWebIn this paper, we study the Atiyah class and the Todd class of the DG manifold [Formula presented] corresponding to an integrable distribution [Formula presented], where [Formula presented] or ℂ. We show that these two classes are canonically identical to those of the Lie pair [Formula presented]. scipher ewasteWebOct 10, 2024 · A celebrated theorem of Kapranov states that the Atiyah class of the tangent bundle of a complex manifold X makes T X [−1] into a Lie algebra object in D + (X), the bounded below derived ... prayer for protection and strengthWebThe Atiyah class was originally introduced by M. F. Atiyah [1] in order to describe the obstruction of the existence of a holomorphic connection on a holomorphic vector bundle. In the late 1990’s, Kontsevich [9] and Kapranov [8] revealed the relation between Atiyah class and Rozansky-Witten scipher bioWebSep 23, 2024 · Pullback for Atiyah classes? In his paper "Complex analytic connections in fibre bundles" Atiyah defines his famous Atiyah class at ( E) ∈ H 1 ( X, End ( E) ⊗ Ω X … sciphe hipWebAug 20, 2009 · We give a universal approach to the deformation-obstruction theory of objects of the derived category of coherent sheaves over a smooth projective family. We … prayer for protection during travelWebSir Michael Francis Atiyah OM FRS FRSE FMedSci FAA FREng (/ ə ˈ t iː ə /; 22 April 1929 – 11 January 2024) was a British-Lebanese mathematician specialising in geometry. His contributions include the Atiyah–Singer … scipher living