On the Betti numbers of the real part of a three-dimensional torus embedding

Jan Ratajski

ArticleOriginal scientific text

Title

On the Betti numbers of the real part of a three-dimensional torus embedding

Authors ¹

Affiliations

Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Abstract

Let X be the three-dimensional, complete, nonsingular, complex torus embedding corresponding to a fan

S \subseteq ℝ^{3}

and let V be the real part of X (for definitions see [1] or [3]). The aim of this note is to give a simple combinatorial formula for calculating the Betti numbers of V.

J. Jurkiewicz, Torus embeddings, polyhedra, k*-actions and homology, Dissertationes Math. 236 (1985).
G. Kempf, F. Knudsen, D. Mumford and B. Saint-Donat, Toroidal Embeddings I, Lecture Notes in Math. 339, Springer, 1973.
T. Oda, Convex Bodies and Algebraic Geometry, Springer, 1980.
J. Stillwell, Classical Topology and Combinatorial Group Theory, Springer, 1980.

Title

On the Betti numbers of the real part of a three-dimensional torus embedding

Affiliations

Abstract

Bibliography