branch in topology: The piecewise linear topology (short PL-topology). The Hauptvermutung (German for main conjecture) states that two triangulations always...

Euclidean spaces into simplices Triangulation (topology), generalizations to topological spaces other than Rd Point-set triangulation, division of the convex...

Algorithmic topology, or computational topology, is a subfield of topology with an overlap with areas of computer science, in particular, computational...

complexes (that are not necessarily simplicial). There is an unshellable triangulation of the tetrahedron. Björner, Anders (1984). "Some combinatorial and...

one of its vertices. Pure simplicial complexes can be thought of as triangulations and provide a definition of polytopes. A facet is a maximal simplex...

Basener, William F. (2006-10-20). Topology and Its Applications. Wiley. pp. 3–14. ISBN 978-0-471-68755-9. Weisstein, Eric W. "Triangulation". MathWorld....

This is a list of algebraic topology topics. Simplex Simplicial complex Polytope Triangulation Barycentric subdivision Simplicial approximation theorem...

PL-sphere. See Triangulation (topology) § Piecewise linear structures for details. Lurie, Jacob (February 13, 2009), Whitehead Triangulations (Lecture 3)...

important tool in algebraic topology. The barycentric subdivision is an operation on simplicial complexes. In algebraic topology it is sometimes useful to...

working knowledge of calculus and topology. After a line, a circle is the simplest example of a topological manifold. Topology ignores bending, so a small piece...

mathematics, Sperner's lemma is a combinatorial result on colorings of triangulations, analogous to the Brouwer fixed point theorem, which is equivalent to...

Locally constant function Trivial topology Cofinite topology Cocountable topology Finer topology Product topology Restricted product Quotient space Unit...

universal 5-manifold with respect to simplicial triangulations". Geometric Topology (Proceedings Georgia Topology Conference, Athens Georgia, 1977). New York-London:...

rational B-spline Point cloud Polygon mesh Triangulation (topology) Triangulation (geometry) Delaunay triangulation Triangulated irregular network v t e...

having a triangulation. However, some 4-manifolds do not have a triangulation, and in general for n > 4 some n-manifolds have triangulations that are...

of this term in mathematics, and so the concept can refer to a triangulation in topology, or a piecewise linear manifold, or one of several different functors...

S2X (with a triangulation derived by applying the double suspension operation to a triangulation of X) is an example of a triangulation of a topological...

properties and concepts in algebraic topology in mathematics. See also: glossary of topology, list of algebraic topology topics, glossary of category theory...

3-manifold theory is considered a part of low-dimensional topology or geometric topology. A key idea in the theory is to study a 3-manifold by considering...

of a regular octahedron, with a triangular boundary. Every abstract triangulation of the projective plane can be embedded into 3D as a polyhedral Möbius...

JTS Topology Suite (Java Topology Suite) is an open-source Java software library that provides an object model for Euclidean planar linear geometry together...

In geometric topology, a branch of mathematics, Moise's theorem, proved by Edwin E. Moise in Moise (1952), states that any topological 3-manifold has an...

University of California, Berkeley who specializes in low-dimensional topology. Together with Laurent C. Siebenmann he developed the Kirby–Siebenmann...

of simplifications to find a locally minimal ideal triangulation. Once a suitable ideal triangulation is found, SnapPea can try to find a hyperbolic structure...

The Hauptvermutung of geometric topology is a now refuted conjecture asking whether any two triangulations of a triangulable space have subdivisions that...

differential topology. The following three glossaries are closely related: Glossary of general topology Glossary of algebraic topology Glossary of Riemannian...

of the Borsuk–Ulam theorem, named after Albert W. Tucker. Let T be a triangulation of the closed n-dimensional ball B n {\displaystyle B_{n}} . Assume...

normal surfaces. In an almost normal surface, one tetrahedron in the triangulation has a single exceptional piece. This is either an octagon that separates...

mathematician, working in gauge theory, symplectic geometry, and low-dimensional topology. He is currently a professor of mathematics at Stanford University. Manolescu...

to preserve the topology of the trilinear interpolant. In his work, Chernyaev extends to 33 the number of cases in the triangulation lookup table. He...