Equivariant principal bundles for G–actions and G–connections

• Autorzy: Indranil Biswas , S. Senthamarai Kannan , D. S. Nagaraj
• Języki publikacji: EN

Abstrakty

EN

Given a complex manifold M equipped with an action of a group G, and a holomorphic principal H–bundle EH on M, we introduce the notion of a connection on EH along the action of G, which is called a G–connection. We show some relationship between the condition that EH admits a G–equivariant structure and the condition that EH admits a (flat) G–connection. The cases of bundles on homogeneous spaces and smooth toric varieties are discussed.

Słowa kluczowe

EN

Equivariant bundles; G–connection; flatness; toric variety

• Wydawca: De Gruyter Open
• Czasopismo: Complex Manifolds
• Rocznik: 2015
• Tom: 2
• Numer: 1

Daty

otrzymano

2015-07-18

zaakceptowano

2015-12-18

online

2015-12-21

Twórcy

autor

Indranil Biswas

• School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha
  Road, Mumbai 400005, India

autor

S. Senthamarai Kannan

• Chennai Mathematical Institute, H1, SIPCOT IT Park, Siruseri, Kelambakkam 603103, India

autor

D. S. Nagaraj

• The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India

Bibliografia

• [1] M. F. Atiyah, Complex analytic connections in fibre bundles, Trans. Amer. Math. Soc. 85 (1957), 181–207.
• [2] I Biswas, A. Dey and M. Poddar, Equivariant principal bundles and logarithmic connections on toric varieties, Pacific Jour.Math. (to appear), arXiv:1507.02415.
• [3] N. Bourbaki, ´El´ements demath´ematique. XXVI. Groupes et alg`ebres de Lie. Chapitre 1: Alg`eebres de Lie, Actualit´es Sci. Ind.No. 1285, Hermann, Paris 1960.
• [4] I. Moerdijk and J. Mrˇcun, Introduction to foliations and Lie groupoids, Cambridge Studies in Advanced Mathematics, 91,Cambridge University Press, Cambridge, 2003.

Identyfikatory

DOI

10.1515/coma-2015-0013