Skip to main content

Braid Monodromy Type Invariants of Surfaces and 4-Manifolds

  • Chapter
Trends in Singularities

Part of the book series: Trends in Mathematics ((TM))

Abstract

In this paper we present the Braid Monodromy Type (BMT) of curves and surfaces. The BMT can distinguish between non-isotopic curves; between different families of surfaces of general type; between connected components of moduli space of surfaces finer than Sieberg-Witten invariants; and between symplectic 4-manifolds.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
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. M. Amram and M. Teicher, Braid monodromy of special algebraic curves, Journal of Knot Theory and its Ramifications, 10 (2) (2001), 171–212.

    Article  MathSciNet  MATH  Google Scholar 

  2. D. Auroux, Symplectic 4 - manifolds as branched coverings of CP 2, Invent. Math., 139 (3) (2000), 551–602.

    MathSciNet  MATH  Google Scholar 

  3. E. Artin, Theory of braids, Ann. Math., 48 (1947), 101–126.

    Article  MathSciNet  MATH  Google Scholar 

  4. Y. Ben-Yitzhak and M. Teicher, Hurwitz equivalence in B3, to appear in International Journal of Algebra and Computation.

    Google Scholar 

  5. Y. Ben-Yitzhak and M. Teicher, Properties of Hurwitz equivalence in the braid group of order n, submitted.

    Google Scholar 

  6. Y. Ben-Yitzhak and M. Teicher, An algorithm for determining conjugation, word equality and HE of half-twists,preprint.

    Google Scholar 

  7. Y. Ben-Yitzhak and M. Teicher, Graph theoretic methods for determining non-Hurwitz equivalence in the braid group and symmetric group, preprint.

    Google Scholar 

  8. C. Ciliberto, H. Miranda and M. Teicher, Braid monodromy factorization of branch curves of KS-surfaces, in preparation.

    Google Scholar 

  9. D. Garber and M. Teicher, The fundamental group’s structure of the complement of some configurations of real line arrangements, Complex Analysis and Algebraic Geometry, Edited by T. Peternell and F.-O. Schreyer, De Gruyter, 2000, 173–223.

    Google Scholar 

  10. D. Garber, S. Kaplan and M. Teicher, A new algorithm for solving the word problem in braid groups, to appear in Advances in Math.

    Google Scholar 

  11. D. Garber, M. Teicher and U. Vishne, xi-classification of arrangements with up to 8 lines, submitted.

    Google Scholar 

  12. D. Garber, M. Teicher and U. Vishne, Classes of wiring diagrams and their invariants, submitted.

    Google Scholar 

  13. S. Kaplan and M. Teicher, Solving the braid word problem via the fundamental group, preprint.

    Google Scholar 

  14. S. Kaplan and M. Teicher, Identifying half-twists using randomized algorithm methods, preprint.

    Google Scholar 

  15. Vik.S. Kulikov, A geometric realization of C-groups, Izvestiya: Math., 45 (1) (1995), 197–206.

    Article  MathSciNet  Google Scholar 

  16. Vik. Kulikov, On Chisini’s Conjecture, Izvestiya: Math., 63 (1999), 1139–1170.

    Article  MathSciNet  MATH  Google Scholar 

  17. Vik. Kulikov and M. Teicher, Braid monodromy factorizations and diffeomorphism types, Izvestiya: Math., 64 (2) (2000), 311–341.

    Google Scholar 

  18. A. Libgober and M. Teicher, Invariants of braid monodromy from representation of Hecke algebra, preprint.

    Google Scholar 

  19. B. Moishezon and M. Teicher, Existence of simply connected algebraic surfaces of positive and zero indices, Proceedings of the National Academy of Sciences, United States of America, 83 (1986), 6665–6666.

    Google Scholar 

  20. B. Moishezon and M. Teicher, Simply connected algebraic surfaces of positive index, Invent. Math., 89 (1987), 601–643.

    Google Scholar 

  21. B. Moishezon and M. Teicher, Braid group techniques in complex geometry, I, Line arrangements in CP2, Contemp. Math., 78 (1988), 425–555.

    MathSciNet  Google Scholar 

  22. B. Moishezon and M. Teicher, Braid group techniques in complex geometry,II, From arrangements of lines and conics to cuspidal curves, Algebraic Geometry, Lect. Notes Math., 1479 (1990) Springer.

    Google Scholar 

  23. A. Robb and M. Teicher, Applications of braid group techniques to the decomposition of moduli spaces, new examples, Topology and its Appl., 78 (1997), 143–151.

    Article  MathSciNet  MATH  Google Scholar 

  24. S. Tan and M. Teicher, On the moduli of the branch curve of a generic triple covering, in preparation.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer Basel AG

About this chapter

Cite this chapter

Teicher, M. (2002). Braid Monodromy Type Invariants of Surfaces and 4-Manifolds. In: Libgober, A., Tibăr, M. (eds) Trends in Singularities. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8161-6_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-8161-6_10

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9461-6

  • Online ISBN: 978-3-0348-8161-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics