Skip to main content
SpringerLink
Log in

Tailoring a Pair of Pants: The Phase Tropical Version

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

We show that the phase tropical pair-of-pants ⊂ (ℂ*)n is (ambient) isotopic to the complex pair-of-pants P° ⊂ (ℂ*)n. The existence of an isotopy between the complex and ober-tropical pairs-of-pants was recently established by the author jointly with H. Ruddat. Thereby all the three (complex, phase tropical, and ober-tropical) versions are isotopic.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. Mikhalkin, “Decomposition into pairs-of-pants for complex algebraic hypersurfaces,” Topology 43, No. 5, 1035–1065 (2004).

    Article  MathSciNet  Google Scholar 

  2. O. Ya. Viro, “On basic concepts of tropical geometry,” Proc. Steklov Inst. Math. 273, 252–282 (2011).

    Article  MathSciNet  Google Scholar 

  3. H. Ruddat and I. Zharkov, Tailoring a Pair-of-Pants, arxiv.org/abs/2001.08267 (2020).

  4. A. Strominger, S.-T. Yau, and E. Zaslow, “Mirror symmetry is T-duality,” Nucl. Phys. B479, No. 1-2, 243–259 (1996).

  5. M. Gross, “Topological mirror symmetry,” Invent. Math. 144, No. 1, 75–137 (2001).

    Article  MathSciNet  Google Scholar 

  6. H. Ruddat and I. Zharkov, Compactifying Torus Fibrations over Integral Affine Manifolds with Singularities, arxiv.org/abs/2003.08521 (2020).

  7. G. Kerr and I. Zharkov, “Phase tropical hypersurfaces,” Geom. Topol. 22, No. 6, 3287–3320 (2018).

    Article  MathSciNet  Google Scholar 

  8. I. M. Gelfand, M. M. Kapranov, and A. V. Zelevinsky, Discriminants, Resultants, and Multidimensional Determinants, Birkhäuser, Boston, MA (1994).

  9. C. P. Rourke and B. J. Sanderson, Introduction to Piecewise-Linear Topology, Springer, Berlin etc. (1972).

    Book  Google Scholar 

  10. R. Caputo, “The isotopy problem for the phase tropical line,” Beitr. Algebra Geom. 61, No. 1, 89–116 (2020).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kansas State University, 138, Cardwell Hall, Manhattan, 66506, USA

    I. Zharkov

Authors
  1. I. Zharkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. Zharkov.

Additional information

Translated from Problemy Matematicheskogo Analiza 105, 2020, pp. 101-109.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zharkov, I. Tailoring a Pair of Pants: The Phase Tropical Version. J Math Sci 250, 300–309 (2020). https://doi.org/10.1007/s10958-020-05016-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-020-05016-4

Search

Navigation