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Topological Immersions and PL Immersions (Combinatorial Topology)

Topological Immersions and PL Immersions (Combinatorial Topology)
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Fast Combinatorial Vector Field Topology

IEEE Transactions on Visualization and Computer Graphics, 2011
This paper introduces a novel approximation algorithm for the fundamental graph problem of combinatorial vector field topology (CVT). CVT is a combinatorial approach based on a sound theoretical basis given by Forman's work on a discrete Morse theory for dynamical systems.
Íngrid Hotz
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Combinatorial Topology Versus Point-Set Topology

History of Topology, 2001
Point-set topology seems to have become separated from the rest of topology around the middle of the twentieth century. For most of the period we shall be considering in this article the term combinatorial topology meantl “practically everything which could not better be described as point-set topology”.
James I M
exaly   +2 more sources

Elements of Combinatorial Topology

2014
Maurice Herlihy, Sérgio Rajsbaum
exaly   +2 more sources

Combinatorial topology and geometry of fracture networks

Physical Review E, 2022
A map is proposed from the space of planar surface fracture networks to a four-parameter mathematical space, summarizing the average topological connectivity and geometrical properties of a network idealized as a convex polygonal mesh. The four parameters are identified as the average number of nodes and edges, the angular defect with respect to ...
A. Roy, R. A. I. Haque, A. J. Mitra, S. Tarafdar, T. Dutta   +4 more
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Some Combinatorial Lemmas in Topology

IBM Journal of Research and Development, 1960
For many years it has been known that a combinatorial result, called the Sperner Lemma, provides an elegant proof of the Brouwer Fixed Point Theorem. Although the proof is elementary, its complete formal exposition depends upon the somewhat complicated operation of subdividing a simplex.
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Intuitive Combinatorial Topology

2001
1 Topology of Curves.- 2 Topology of Surfaces.- 3 Homotopy and Homology.- Appendix A: Topological Objects in Nematic Liquid Crystals.- A.1. Nematics.- A.2. Disclination in the Nematic.- A.3. Disclination and Topology.- A.4. Singular Points.- A.5. What Else Is There?.
V. G. Boltyanskiĭ, V. A. Efremovich
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Combinatorial Topology and Digital Topology

2014
Topology is the study of the equivalence between two general spaces under continuous mappings. Two spaces are called homemorphic if there is an invertible continuous function between them. Triangles or simplexes are used in topological analysis of a space since we want to decompose a complex space into some simpler shapes to better understanding the ...
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Combinatorial Topology of Surfaces

Mathematics Magazine, 1955
Tlhe first section of this paper will be devoted to the study of two particular surfaces. The methods used to treat thiese surfaces will then be extended to develop a classificationof surfaces, each class consisting of combinatorially eauivalent surfaces.
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On Duality in Combinatorial Topology

1991
The boundary of an r-dimensional algebraic complex is an (r - 1)-dimensional algebraic complex [2]. Along with the operation of passing to the boundary, we consider the dual operation, which associates with each r-dimensional algebraic complex an (r + 1)-dimensional complex.
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