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Everything about Homotopy
Continuous deformation between two continuous functions
In topology, two continuous functions from one topological space to another are called homotopic if one can be "continuously deformed" into the other, such a deformation being called a homotopy between the two functions. A notable use of homotopy is the definition of homotopy groups and cohomotopy groups, important invariants in algebraic topology. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: HomotopyA 5-minute orientation
- Skim a recent paper: Natural Convection Non-Newtonian EMHD Dissipative Flow Through a Microchannel Containing a Non-Darcy Porous Medium: Homotopy Perturbation Method StudyInfluential work since 2022
- Pick up a classic book: The Mathematical works of J. H. C. WhiteheadThe most-reprinted book on the subject
- Read the landmark paper: Homotopy perturbation techniqueCited 2,601 times
- Go sideways: Path (topology)A closely related topic
- Go sideways: Fundamental groupA closely related topic
📖 Definitions
Noun A continuous deformation of one continuous function or map to another.
Noun The relationship between two continuous functions where homotopy from one to the other is evident.
Noun Ellipsis of homotopy theory (“the systematic study of homotopies and their equivalence classes”).
Noun A theory associating a system of groups with each topological space.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Homotopy perturbation technique
A coupling method of a homotopy technique and a perturbation technique for non-linear problems
On the homotopy analysis method for nonlinear problems
Homotopy perturbation method: a new nonlinear analytical technique
Application of homotopy perturbation method to nonlinear wave equations
An optimal homotopy-analysis approach for strongly nonlinear differential equations
Homotopy perturbation method for solving boundary value problems
Growing Together and Growing Apart: Regional and Sex Differences in the Lifespan Developmental Trajectories of Functional Homotopy
🆕 Influential since 2022
Natural Convection Non-Newtonian EMHD Dissipative Flow Through a Microchannel Containing a Non-Darcy Porous Medium: Homotopy Perturbation Method Study
Homotopy perturbation method for strongly nonlinear oscillators
Heat and mass exchanger analysis for Ree-Eyring hybrid nanofluid through a stretching sheet utilizing the homotopy perturbation method
On Trajectory Homotopy to Explore and Penetrate Dynamically of Multi-UAV
Static homotopy response analysis of structure with random variables of arbitrary distributions by minimizing stochastic residual error
📚 Books worth reading
The Mathematical works of J. H. C. WhiteheadJohn Henry Constantine Whitehead, Ioan Mackenzie James · 1962
Beyond perturbationShijun Liao · 2003- 📕Handbook of Homotopy TheoryHaynes Miller · 2019
- 📕Illustrated Introduction to Topology and HomotopySasho Kalajdzievski · 2012
Homotopy theoryGeorge W. Whitehead · 1950
Directed algebraic topologyMarco Grandis · 2009- 📕Categorical Homotopy TheoryEmily Riehl · 2014
Advances in Homotopy TheoryW. Sutherland, J. W. S. Cassels · 1989
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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