IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-031-54172-8_8.html

The Riemann-Hilbert Correspondence for Rank 2 Meromorphic Connections on Curves

In: Handbook of Geometry and Topology of Singularities VI: Foliations

Author

Listed:
  • Frank Loray

    (Univ Rennes, CNRS, IRMAR, UMR 6625)

Abstract

The goal of this text is to introduce the Riemann-Hilbert correspondence in the rank two case and irregular setting over ℂ $$\mathbb C$$ . This establishes a one-to-one correspondence between isomorphism classes of rank two vector bundles with meromorphic linear connections on curves, and some representation of fundamental groups or groupoids on the corresponding Riemann surface with punctures, up to some natural equivalence. The goal of this text is to provide a self-contained approach with proofs accessible for a master student, in particular including the ramified case. We omit a great part of the huge literature on this beautiful subject.

Suggested Citation

  • Frank Loray, 2024. "The Riemann-Hilbert Correspondence for Rank 2 Meromorphic Connections on Curves," Springer Books, in: Felipe Cano & José Luis Cisneros-Molina & Lê Dũng Tráng & José Seade (ed.), Handbook of Geometry and Topology of Singularities VI: Foliations, chapter 0, pages 267-305, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-54172-8_8
    DOI: 10.1007/978-3-031-54172-8_8
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-031-54172-8_8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.