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Cohomology of torus manifold bundles

  • Jyoti Dasgupta EMAIL logo , Bivas Khan and Vikraman Uma
Published/Copyright: May 21, 2019
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 69 Issue 3

Abstract

Let X be a 2n-dimensional torus manifold with a locally standard T ≅ (S1)n action whose orbit space is a homology polytope. Smooth complete complex toric varieties and quasitoric manifolds are examples of torus manifolds. Consider a principal T-bundle p : E → B and let π : E(X) → B be the associated torus manifold bundle. We give a presentation of the singular cohomology ring of E(X) as a H*(B)-algebra and the topological K-ring of E(X) as a K*(B)-algebra with generators and relations. These generalize the results in [17] and [19] when the base B = pt. These also extend the results in [20], obtained in the case of a smooth projective toric variety, to any smooth complete toric variety.

MSC 2010: Primary 55N15; 57S25
Keywords: torus manifold bundles; cohomology; K-theory

  1. (Communicated by Július Korbaš)

Acknowledgement

The authors are grateful to Prof. P. Sankaran for drawing our attention to this problem and for his valuable comments on the initial versions of this manuscript. The first and the second author thank the Council of Scientific and Industrial Research (CSIR) for their financial support. The authors wish to thank the unknown referee for a careful reading of the manuscript and for very valuable comments and suggestions which led to improving the text. The final section has been added taking into account the referee’s suggestions. The extension of Theorem 3.3 to Theorem 6.1 was also suggested by Prof. M. Masuda in a prior email correspondence. We are grateful to him for this.

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Received: 2018-04-17
Accepted: 2018-09-02
Published Online: 2019-05-21
Published in Print: 2019-06-26

© 2019 Mathematical Institute Slovak Academy of Sciences

Articles in the same Issue

  1. Regular papers
  2. The life jubilee of Prof. RNDr. Sylvia Pulmannová, DrSc.
  3. Perfect 1-factorizations
  4. A topological duality for strong Boolean posets
  5. On the Diophantine equations x2 + 2α 3β 19γ = yn and x2 + 2α 3β 13γ = yn
  6. Tribonacci numbers and primes of the form p = x2 + 11y2
  7. Basic semirings
  8. A conjecture for varieties of completely regular semigroups
  9. Uniqueness of meromorphic function with its shift operator under the purview of two or three shared sets
  10. Differential subordination results for Mittag-Leffler type functions with bounded turning property
  11. Mittag-Leffler stability for non-instantaneous impulsive Caputo fractional differential equations with delays
  12. Asymptotically periodic behavior of solutions of fractional evolution equations of order 1 < α < 2
  13. On the polynomial entropy for morse gradient systems
  14. Quantitative approximation by Stancu-Durrmeyer-Choquet-Šipoš operators
  15. A note on non-linear ∗-Jordan derivations on ∗-algebras
  16. Disjoint hypercyclic weighted translations on locally compact hausdorff spaces
  17. Some new results on real hypersurfaces with generalized Tanaka-Webster connection
  18. Relative topological properties of hyperspaces
  19. Cohomology of torus manifold bundles
  20. The Menger and projective Menger properties of function spaces with the set-open topology
  21. Asymptotic behavior of the record values in a stationary Gaussian sequence, with applications
https://doi.org/10.1515/ms-2017-0257
Keywords for this article
torus manifold bundles; cohomology; K-theory

Articles in the same Issue

  1. Regular papers
  2. The life jubilee of Prof. RNDr. Sylvia Pulmannová, DrSc.
  3. Perfect 1-factorizations
  4. A topological duality for strong Boolean posets
  5. On the Diophantine equations x2 + 2α 3β 19γ = yn and x2 + 2α 3β 13γ = yn
  6. Tribonacci numbers and primes of the form p = x2 + 11y2
  7. Basic semirings
  8. A conjecture for varieties of completely regular semigroups
  9. Uniqueness of meromorphic function with its shift operator under the purview of two or three shared sets
  10. Differential subordination results for Mittag-Leffler type functions with bounded turning property
  11. Mittag-Leffler stability for non-instantaneous impulsive Caputo fractional differential equations with delays
  12. Asymptotically periodic behavior of solutions of fractional evolution equations of order 1 < α < 2
  13. On the polynomial entropy for morse gradient systems
  14. Quantitative approximation by Stancu-Durrmeyer-Choquet-Šipoš operators
  15. A note on non-linear ∗-Jordan derivations on ∗-algebras
  16. Disjoint hypercyclic weighted translations on locally compact hausdorff spaces
  17. Some new results on real hypersurfaces with generalized Tanaka-Webster connection
  18. Relative topological properties of hyperspaces
  19. Cohomology of torus manifold bundles
  20. The Menger and projective Menger properties of function spaces with the set-open topology
  21. Asymptotic behavior of the record values in a stationary Gaussian sequence, with applications
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