Proceedings of the Japan Academy, Series A, Mathematical Sciences

The number of small covers over cubes and the product of at most three simplices up to equivariant cobordism

Yanchang Chen and Yanying Wang

Full-text: Open access

Abstract

The equivariant cobordism class of a small cover over a simple convex polytope is determined by its tangential representation set. Since the tangential representation can be identified with the characteristic function of the simple convex polytope, by using characteristic functions we determine the number of small covers over cubes and the product of at most three simplices up to equivariant cobordism.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 87, Number 6 (2011), 95-98.

Dates
First available in Project Euclid: 1 June 2011

Permanent link to this document
https://projecteuclid.org/euclid.pja/1306934065

Digital Object Identifier
doi:10.3792/pjaa.87.95

Mathematical Reviews number (MathSciNet)
MR2803888

Zentralblatt MATH identifier
1231.57028

Subjects
Primary: 57R85: Equivariant cobordism
Secondary: 05C10: Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25]

Keywords
Cobordism small cover tangential representation

Citation

Chen, Yanchang; Wang, Yanying. The number of small covers over cubes and the product of at most three simplices up to equivariant cobordism. Proc. Japan Acad. Ser. A Math. Sci. 87 (2011), no. 6, 95--98. doi:10.3792/pjaa.87.95. https://projecteuclid.org/euclid.pja/1306934065


Export citation

References

  • M. Cai, X. Chen and Z. Lü, Small covers over prisms, Topology Appl. 154 (2007), no. 11, 2228–2234.
  • S. Choi, The number of small covers over cubes, Algebr. Geom. Topol. 8 (2008), no. 4, 2391–2399.
  • S. Choi, The number of orientable small covers over cubes, Proc. Japan Acad. Ser. A Math. Sci. 86 (2010), no. 6, 97–100.
  • M. W. Davis and T. Januszkiewicz, Convex polytopes, Coxeter orbifolds and torus actions, Duke Math. J. 62 (1991), no. 2, 417–451.
  • Z. Lü, 2-torus manifolds, cobordism and small covers, Pacific J. Math. 241 (2009), no. 2, 285–308.
  • Z. Lü and Q. Tan, A differential operator and tom Dieck-Kosniowski-Stong localization theorem, arXiv:1008.2166.
  • R. E. Stong, Equivariant bordism and $(Z_{2})^{k}$ actions, Duke Math. J. 37 (1970), 779–785.