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

Colloquium Mathematicae (1993)

- Volume: 64, Issue: 1, page 59-64
- ISSN: 0010-1354

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topRatajski, Jan. "On the Betti numbers of the real part of a three-dimensional torus embedding." Colloquium Mathematicae 64.1 (1993): 59-64. <http://eudml.org/doc/210173>.

@article{Ratajski1993,

abstract = {Let X be the three-dimensional, complete, nonsingular, complex torus embedding corresponding to a fan $S ⊆ ℝ^\{3\}$ 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.},

author = {Ratajski, Jan},

journal = {Colloquium Mathematicae},

keywords = {semi-algebraic geometry; toric variety; compact manifold; Betti numbers; fundamental group},

language = {eng},

number = {1},

pages = {59-64},

title = {On the Betti numbers of the real part of a three-dimensional torus embedding},

url = {http://eudml.org/doc/210173},

volume = {64},

year = {1993},

}

TY - JOUR

AU - Ratajski, Jan

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

JO - Colloquium Mathematicae

PY - 1993

VL - 64

IS - 1

SP - 59

EP - 64

AB - Let X be the three-dimensional, complete, nonsingular, complex torus embedding corresponding to a fan $S ⊆ ℝ^{3}$ 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.

LA - eng

KW - semi-algebraic geometry; toric variety; compact manifold; Betti numbers; fundamental group

UR - http://eudml.org/doc/210173

ER -

## References

top- [1] J. Jurkiewicz, Torus embeddings, polyhedra, k*-actions and homology, Dissertationes Math. 236 (1985). Zbl0599.14014
- [2] G. Kempf, F. Knudsen, D. Mumford and B. Saint-Donat, Toroidal Embeddings I, Lecture Notes in Math. 339, Springer, 1973. Zbl0271.14017
- [3] T. Oda, Convex Bodies and Algebraic Geometry, Springer, 1980.
- [4] J. Stillwell, Classical Topology and Combinatorial Group Theory, Springer, 1980.

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