Skip to main content
×
Home
    • Aa
    • Aa
  • Access
  • Cited by 33
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Biswas, Indranil and Gammelgaard, Niels Leth 2016. Vassiliev invariants from symmetric spaces. Journal of Knot Theory and Its Ramifications, p. 1650055.


    Chen, Zhuo Stiénon, Mathieu and Xu, Ping 2016. From Atiyah Classes to Homotopy Leibniz Algebras. Communications in Mathematical Physics, Vol. 341, Issue. 1, p. 309.


    Bandiera, Ruggero 2015. Formality of Kapranov's Brackets in Kähler Geometry via Pre-Lie Deformation Theory. International Mathematics Research Notices, p. rnv362.


    Dolgushev, Vasily Rogers, Chris and Willwacher, Thomas 2015. Kontsevich's graph complex, GRT, and the deformation complex of the sheaf of polyvector fields. Annals of Mathematics, p. 855.


    Mehta, Rajan Amit Stiénon, Mathieu and Xu, Ping 2015. The Atiyah class of a dg-vector bundle. Comptes Rendus Mathematique, Vol. 353, Issue. 4, p. 357.


    Orem, Hendrik 2015. Formal geometry for noncommutative manifolds. Journal of Algebra, Vol. 434, p. 261.


    Polesello, Pietro 2015. On quantizations of complex contact manifolds. Advances in Mathematics, Vol. 268, p. 129.


    Voglaire, Yannick and Xu, Ping 2015. Rozansky–Witten-Type Invariants from Symplectic Lie Pairs. Communications in Mathematical Physics, Vol. 336, Issue. 1, p. 217.


    Calaque, Damien Căldăraru, Andrei and Tu, Junwu 2014. On the Lie algebroid of a derived self-intersection. Advances in Mathematics, Vol. 262, p. 751.


    Chen, Zhuo Stiénon, Mathieu and Xu, Ping 2014. A Hopf algebra associated with a Lie pair. Comptes Rendus Mathematique, Vol. 352, Issue. 11, p. 929.


    Gwilliam, Owen and Grady, Ryan 2014. One-dimensional Chern–Simons theory and theÂgenus. Algebraic & Geometric Topology, Vol. 14, Issue. 4, p. 2299.


    Gwilliam, Owen and Grady, Ryan 2014. One-dimensional Chern–Simons theory and theÂgenus. Algebraic & Geometric Topology, Vol. 14, Issue. 4, p. 2299.


    Polishchuk, Alexander and Tu, Junwu 2014. DG-resolutions of NC-smooth thickenings and NC-Fourier–Mukai transforms. Mathematische Annalen, Vol. 360, Issue. 1-2, p. 79.


    Calaque, Damien Căldăraru, Andrei and Tu, Junwu 2013. for an inclusion of Lie algebras. Journal of Algebra, Vol. 378, p. 64.


    Källén, Johan Qiu, Jian and Zabzine, Maxim 2013. Equivariant Rozansky–Witten classes and TFTs. Journal of Geometry and Physics, Vol. 64, p. 222.


    Rumynin, D. A. 2013. Lie algebras in symmetric monoidal categories. Siberian Mathematical Journal, Vol. 54, Issue. 5, p. 905.


    Arinkin, Dima and Căldăraru, Andrei 2012. When is the self-intersection of a subvariety a fibration?. Advances in Mathematics, Vol. 231, Issue. 2, p. 815.


    Calaque, Damien Rossi, Carlo and van den Bergh, Michel 2012. Căldăraru's conjecture and Tsygan's formality. Annals of Mathematics, Vol. 176, Issue. 2, p. 865.


    Laurent-Gengoux, Camille Stiénon, Mathieu and Xu, Ping 2012. Exponential map and algebra associated to a Lie pair. Comptes Rendus Mathematique, Vol. 350, Issue. 17-18, p. 817.


    Qiu, Jian and Zabzine, Maxim 2012. Knot invariants and new weight systems from general 3D TFTs. Journal of Geometry and Physics, Vol. 62, Issue. 2, p. 242.


    ×

Rozansky–Witten invariants via Atiyah classes

  • M. KAPRANOV (a1)
  • DOI: http://dx.doi.org/10.1023/A:1000664527238
  • Published online: 01 January 1999
Abstract

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. We give a simple cohomological definition of these weights in terms of the Atiyah class of X (the obstruction to the existence of a holomorphic connection). We show that the analogy between the tensor of curvature of a hyper-Kähler metric and the tensor of structure constants of a Lie algebra observed by Rozansky and Witten, holds in fact for any complex manifold, if we work at the level of cohomology and for any Kähler manifold, if we work at the level of Dolbeault cochains. As an outcome of our considerations, we give a formula for Rozansky–Witten classes using any Kähler metric on a holomorphic symplectic manifold.

    • Send article to Kindle

      To send this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Rozansky–Witten invariants via Atiyah classes
      Your Kindle email address
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      Rozansky–Witten invariants via Atiyah classes
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      Rozansky–Witten invariants via Atiyah classes
      Available formats
      ×
Copyright
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
  • URL: /core/journals/compositio-mathematica
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords: