Triangulating topological spaces

H. Edelsbrunner, N. Shah, International Journal of Computational Geometry and Applications 7 (1997) 365–378.

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Abstract
Given a subspace X subset of or equal to R-d and a finite set S subset of or equal to R-d, we introduce the Delaunay complex, D-X, restricted by X. Its simplices are spanned by subsets T subset of or equal to S for which the common intersection of Voronoi cells meets X in a non-empty set. By the nerve theorem, boolean OR D-X and X are homotopy equivalent if all such sets are contractible. This paper proves a sufficient condition for boolean OR D-X and X be homeomorphic.
Publishing Year
Date Published
1997-01-01
Journal Title
International Journal of Computational Geometry and Applications
Acknowledgement
Partially supported by the National Science Foundation, under grant ASC-200301 and the Alan T. Waterman award, grant CCR-9118874.
Volume
7
Issue
4
Page
365 - 378
IST-REx-ID

Cite this

Edelsbrunner H, Shah N. Triangulating topological spaces. International Journal of Computational Geometry and Applications. 1997;7(4):365-378. doi:10.1142/S0218195997000223
Edelsbrunner, H., & Shah, N. (1997). Triangulating topological spaces. International Journal of Computational Geometry and Applications, 7(4), 365–378. https://doi.org/10.1142/S0218195997000223
Edelsbrunner, Herbert, and Nimish Shah. “Triangulating Topological Spaces.” International Journal of Computational Geometry and Applications 7, no. 4 (1997): 365–78. https://doi.org/10.1142/S0218195997000223.
H. Edelsbrunner and N. Shah, “Triangulating topological spaces,” International Journal of Computational Geometry and Applications, vol. 7, no. 4, pp. 365–378, 1997.
Edelsbrunner H, Shah N. 1997. Triangulating topological spaces. International Journal of Computational Geometry and Applications. 7(4), 365–378.
Edelsbrunner, Herbert, and Nimish Shah. “Triangulating Topological Spaces.” International Journal of Computational Geometry and Applications, vol. 7, no. 4, World Scientific Publishing, 1997, pp. 365–78, doi:10.1142/S0218195997000223.

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