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Everything about Simplicial map
A simplicial map is a function between two simplicial complexes, with the property that the images of the vertices of a simplex always span a simplex. Simplicial maps can be used to approximate continuous functions between topological spaces that can be triangulated; this is formalized by the simplicial approximation theorem. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Simplicial mapA 5-minute orientation
- Skim a recent paper: Contiguity distance between simplicial mapsInfluential work since 2022
- Pick up a classic book: Topology and GeometryThe most-reprinted book on the subject
- Read the landmark paper: On the equivalence relation forced by the singularities of a nondegenerate simplicial mapCited 13 times
- Go sideways: Barycentric subdivisionA closely related topic
- Go sideways: Simplicial approximation theoremA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
On the equivalence relation forced by the singularities of a nondegenerate simplicial map
On the Lusternik–Schnirelmann category of a simplicial map
Simplicial energy and simplicial harmonic maps
Trainable and explainable simplicial map neural networks
Simplicial-Map Neural Networks Robust to Adversarial Examples
Optimizing the Simplicial-Map Neural Network Architecture
A simplicial James–Hopf map and decompositions of the unstable Adams spectral sequence for suspensions
Multiple points of a simplicial map and image-computing spectral sequences
🆕 Influential since 2022
📚 Books worth reading
Topology and GeometryGlen E. Bredon · 1993- 📕TopologyE. M. Patterson · 1956
Grassmannians of classical buildingsMark Pankov · 2010
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Barycentric subdivision In mathematics, the barycentric subdivision is a standard way to subdivide a given simplex into smaller ones. Its extension to simplicial complexes is…
- Simplicial approximation theorem In mathematics, the simplicial approximation theorem is a foundational result for algebraic topology, guaranteeing that continuous mappings can be (by…
- Triangulation (topology) In mathematics, triangulation describes the replacement of topological spaces with simplicial complexes by the choice of an appropriate homeomorphism.…
- Discrete calculus Discrete calculus or the calculus of discrete functions, is the mathematical study of incremental change, in the same way that geometry is the study of…
- Piecewise linear continuation Simplicial continuation, or piecewise linear continuation (Allgower and Georg), is a one-parameter continuation method which is well suited to small to…
- Abstract simplicial complex In combinatorics, an abstract simplicial complex (ASC), often called an abstract complex or just a complex, is a family of sets that is closed under taking…
- Subdivision (simplicial complex) A subdivision (also called refinement) of a simplicial complex is another simplicial complex in which, intuitively, one or more simplices of the original…
- Piecewise linear function In mathematics, a piecewise linear or segmented function is a real-valued function of a real variable, whose graph is composed of straight-line segments…