Skip to main content

Algebraic Differential Characters of Flat Connections with Nilpotent Residues

  • Chapter
  • First Online:
Algebraic Topology

Part of the book series: Abel Symposia ((ABEL,volume 4))

Abstract

We construct unramified algebraic differential characters for flat connections with nilpotent residues along a strict normal crossings divisorp.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Chern SS, Simons J (1974) Characteristic forms and geometric invariants. Ann Math 99:48–68

    Article  MathSciNet  Google Scholar 

  2. Cheeger J, Simons J (1980) Differential characters and geometric invariants. Lecture Notes in Mathematics 1167, Springer, Berlin pp 50–80

    Google Scholar 

  3. Bloch S (1977) Applications of the dilogarithm function in algebraic K-theory and algebraic geometry. International Symposium on Algebraic Geometry, Kyoto, pp 103–114

    Google Scholar 

  4. Cheeger J (1974) Invariants of flat bundles. Proceedings of the International Congress of Mathematicians in Vancouver, vol. 2, pp 3–6

    Google Scholar 

  5. Esnault H (2000) Algebraic differential characters. Regulators in analysis, geometry and number theory, Progress in mathematics, Birkhäuser, vol. 171, pp 89–117

    Google Scholar 

  6. Esnault H, Viehweg E (1986) Logarithmic de Rham complexes and vanishing theorems. Invent math 86:161–194

    Article  MATH  MathSciNet  Google Scholar 

  7. Atiyah M (1956) Complex analytic connections in fiber bundles. Trans Am Math Soc 85:181–207

    Article  MathSciNet  Google Scholar 

  8. Esnault H (1992) Characteristic classes of flat bundles, II. K-Theory 6:45–56

    Article  MATH  MathSciNet  Google Scholar 

  9. Iyer J, Simpson C (2007) Regulators of canonical extensions are torsion: the smooth divisor case, p 41

    Google Scholar 

  10. Bloch S, Esnault H (1997) Algebraic Chern–Simons theory. Am J Math 119:903–952

    Article  MATH  MathSciNet  Google Scholar 

  11. Reznikov A (1995) All regulators of flat bundles are torsion. Ann Math 141(2):373–386

    Article  MATH  MathSciNet  Google Scholar 

  12. Esnault H (1988) Characteristic classes of flat bundles. Topology 27:323–352

    Article  MATH  MathSciNet  Google Scholar 

  13. Deligne P (1970) Équations Différentielles à Points Singuliers Séguliers. Lecture Notes in mathematics vol. 163, Springer, Berlin

    Google Scholar 

  14. Esnault H (2002) Characteristic classes of flat bundles and determinant of the Gauß-Manin connection. Proceedings of the International Congress of Mathematicians, Beijing, Higher Education Press, pp 471–483

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hélène Esnault .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Esnault, H. (2009). Algebraic Differential Characters of Flat Connections with Nilpotent Residues. In: Baas, N., Friedlander, E., Jahren, B., Østvær, P. (eds) Algebraic Topology. Abel Symposia, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01200-6_5

Download citation

Publish with us

Policies and ethics