Live briefing
Everything about CW complex
Type of topological space
In mathematics, and specifically in topology, a CW complex is a topological space that is built by gluing together topological balls of different dimensions in specific ways. The notion generalizes both manifolds and simplicial complexes and has particular significance for algebraic topology. It was initially introduced by J. H. C. Whitehead to meet the needs of homotopy theory. CW complexes have better categorical properties than simplicial complexes, but still retain a combinatorial nature that allows for computation. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: CW complexA 5-minute orientation
- Skim a recent paper: Complex heatmap visualizationInfluential work since 2022
- Pick up a classic book: Ends of complexesThe most-reprinted book on the subject
- Read the landmark paper: Statistical mechanics of complex networksCited 16,460 times
- Go sideways: Cellular homologyA closely related topic
- Go sideways: Graph (topology)A closely related topic
đź“– Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Statistical mechanics of complex networks
The Structure and Function of Complex Networks
UK Biobank: An Open Access Resource for Identifying the Causes of a Wide Range of Complex Diseases of Middle and Old Age
The Unity and Diversity of Executive Functions and Their Contributions to Complex “Frontal Lobe” Tasks: A Latent Variable Analysis
Integrative Analysis of Complex Cancer Genomics and Clinical Profiles Using the cBioPortal
An algorithm for the machine calculation of complex Fourier series
Complex thermoelectric materials
Complex network measures of brain connectivity: Uses and interpretations
🆕 Influential since 2022
Complex heatmap visualization
Common Method Bias: It's Bad, It's Complex, It's Widespread, and It's Not Easy to Fix
The complex role of tumor-infiltrating macrophages
Compositionally complex doping for zero-strain zero-cobalt layered cathodes
Agentic AI: Autonomous Intelligence for Complex Goals—A Comprehensive Survey
đź“š Books worth reading
Ends of complexesBruce Hughes · 1996
Cellular structures in topologyRudolf Fritsch · 1989- 📕CW-complexes, homology theoryRenzo A. Piccinini · 1973
The finitenessobstruction of C.T.C. WallKalathoor Varadarajan · 1989- 📕The topology of CW complexes [by] Albert T. Lundell and Stephen WeingramAlbert T. Lundell · 1969
The topology of CW complexesAlbert T. Lundell · 1969- 📕The paracompactness of the CW-complex and gradient mappings in locally convex spacesMichael John Walsh · 1952
- 📕Torsion decomposition of finite CW-complexesPaul G. Ledergerber · 1971
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
đź”— Related topics
- Cellular homology In mathematics, cellular homology in algebraic topology is a homology theory for the category of CW-complexes. It agrees with singular homology, and can…
- Graph (topology) In topology, a branch of mathematics, a graph is a topological space which arises from a usual graph G = ( E , V ) {\displaystyle G=(E,V)} by replacing…
- Triangulation (topology) In mathematics, triangulation describes the replacement of topological spaces with simplicial complexes by the choice of an appropriate homeomorphism.…
- Homology (mathematics) In mathematics, the term homology, originally introduced in algebraic topology, has three primary, closely related usages. First, there is the homology…
- Hopf invariant In mathematics, in particular in algebraic topology, the Hopf invariant is a homotopy invariant of certain maps between n-spheres. In 1931 Heinz Hopf used…
- Homotopy theory In mathematics, homotopy theory is a systematic study of situations in which maps can come with homotopies between them. It originated as a topic in algebraic…
- Eilenberg–MacLane space In mathematics, specifically algebraic topology, an Eilenberg–MacLane space is a topological space with a single nontrivial homotopy group. Let G be a…
- Glossary of algebraic topology This is a glossary of properties and concepts in algebraic topology in mathematics. See also: glossary of topology, list of algebraic topology topics,…