Torus actions and combinatorics of polytopes

  title={Torus actions and combinatorics of polytopes},
  author={Victor M. Buchstaber and TARAS E. PANOV},
In this work we develop the study of relationship between the algebraic topology of manifolds and the combinatorics of polytopes. Originally, this research was inspired by the results of the toric variety theory. The main object of our study is the smooth manifold defined by the combinatorial structure of a simple polytope. This manifold is equipped with natural action of the compact torus T. We define an n-dimensional convex polytope as a bounded set in R that is obtained as the intersection… CONTINUE READING

From This Paper

Figures, tables, and topics from this paper.


Publications referenced by this paper.
Showing 1-9 of 9 references

Introduction to Toric Varieties

W. Fulton
Princeton Univ. Press • 1993

An introduction to convex polytopes

A. Brønsted
Springer-Verlag New-York • 1983

Combinatorics and Commutative Algebra

R. Stanley
Progress in Mathematics 41, Birkhauser, Boston • 1983

Convex polytopes , Coxeter orbifolds and torus actions , Duke Math

T. Januszkiewicz
Journal • 1978

Hochster, Cohen–Macaulay rings, combinatorics, and simplicial complexes, in Ring Theory II (Proc. Second Oklahoma Conference) (B.R.McDonald and R.Morris

M. Ho


S. Maclane
Springer-Verlag Berlin • 1963

Homological algebra

H. Cartan, S. Eilenberg
Princeton Univ. Press, Princeton, N.J. • 1956

Algebraic topology of manifolds defined by simple polytopes ( Russian ) , Uspekhi Mat

T. E. Panov
Quantum Cohomology Rings of Toric Manifolds , Journées de Géometrie Algébrique d ’ Orsay ( Juillet

Similar Papers

Loading similar papers…