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Journals / Turkish Journal of Mathematics / 2014 / Cilt: 38 - Sayı: 3

Equivariant structure constants for Hamiltonian-T-spaces

Ho-hon LEUNG
Pages
483–491
Publication Date
2014-05-16
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

These formulas can be regarded as a generalization of Tymoczko's results.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:If there exists a set of canonical classes on a compact Hamiltonian-T-space in the sense of R Goldin and S Tolman, we derive some formulas for certain equivariant structure constants in terms of other equivariant structure constants and the values of canonical classes restricted to some fixed points.
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Key Findings & Data:If there exists a set of canonical classes on a compact Hamiltonian-T-space in the sense of R Goldin and S Tolman, we derive some formulas for certain equivariant structure constants in terms of other equivariant structure constants and the values of canonical classes restricted to some fixed points.
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Conclusion & Impact:These formulas can be regarded as a generalization of Tymoczko's results.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Symplectic geometry · moment map · equivariant cohomology

Abstract

If there exists a set of canonical classes on a compact Hamiltonian-T-space in the sense of R Goldin and S Tolman, we derive some formulas for certain equivariant structure constants in terms of other equivariant structure constants and the values of canonical classes restricted to some fixed points. These formulas can be regarded as a generalization of Tymoczko's results.

Özet

If there exists a set of canonical classes on a compact Hamiltonian-T-space in the sense of R Goldin and S Tolman, we derive some formulas for certain equivariant structure constants in terms of other equivariant structure constants and the values of canonical classes restricted to some fixed points. These formulas can be regarded as a generalization of Tymoczko's results.

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Cite This Article

LEUNG, H. (2014). Equivariant structure constants for Hamiltonian-T-spaces. Turkish Journal of Mathematics, Cilt: 38 - Sayı: 3, 483–491. https://ajindex.com/articles/185686

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References (6)

  1. Goldin, R., Tolman, S.: Towards generalizing Schubert calculus in the symplectic category. J. Symplect. Geom. 7, 449–473 (2009)
  2. Guillemin, V., Zara, C.: 1-skeleta, Betti numbers, and equivariant cohomology. Duke Math. J. 107, 283–349 (2001)
  3. Leung, H.H.: K -theory of weight varieties. New York J. Math. 17, 251–267 (2011)
  4. Leung, H.H.: K -theory of weight varieties and divided difference operators in equivariant KK -theory. PhD, Cornell University, 2011
  5. Tymoczko, J.S.: Equivariant structure constants for ordinary and weighted projective space. arXiv:0806.3588v1 [math.AT]
  6. Zara, C.: Positivity of Equivariant Schubert Classes Through Moment Map Degeneration, J. Symplect. Geom. 8, 381–401 (2010).