DOI QR코드

DOI QR Code

THE ORIENTABILITY OF REAL TORIC MANIFOLDS

  • Kim, Jin Hong (Department of Mathematics Education, Chosun University)
  • Received : 2016.07.05
  • Accepted : 2016.12.30
  • Published : 2017.03.25

Abstract

The aim of this short paper is to give a new necessary and sufficient condition, topological in nature, for certain real toric manifolds to be orientable in terms of the connectedness of their particular submanifolds of codimension zero.

Keywords

References

  1. V. Buchstaber and T. Panov, Torus actions and their applications in topology and combinatorics, University Lecture Series, Vol. 24, Amer. Math. Soc., Providence, Rhode Island, 2002.
  2. V. Buchstaber and T. Panov, Toric topology, Math. Surveys and Monograph 204, Amer. Math. Soc., 2015; arXiv:1210.2368v3.
  3. M. Davis and T. Januszkiewicz, Convex polytopes, Coxeter orbifolds and torus actions, Duke Math. J. 61 (1991), 417-451.
  4. H. Kuwata, M. Masuda, and H. Zeng, Torsion in the cohomology of torus orbifolds, preprint (2016); arXiv:1604.03138v1.
  5. Z. Lu and M. Masuda, Equivariant classi cation of 2-torus manifolds, Colloq. Math. 115 (2009), 171-188. https://doi.org/10.4064/cm115-2-3
  6. H. Nakayama and Y. Nishimura, The orientability of small covers and colloring simple polytopes, Osaka J. Math. 42 (2005), 243-256.
  7. E. Soprunova and F. Sottile, Lower bounds in real algebraic geometry and ori- entability of real toric varieties, Discrete Comput. Geom. 50 (2013), 509-519. https://doi.org/10.1007/s00454-013-9498-9
  8. D. Yeroshkin, On Poincare duality for orbifolds, preprint(2015); arXiv:1502.03384.