Stable homotopy theory
Stable homotopy theory In mathematics, stable homotopy theory is a branch of algebraic topology. Stability ... the Freudenthal suspension theorem. In general, stable homotopy theory tries to isolate the phenomena ...
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Spectrum (homotopy theory)
Spectrum (homotopy theory) In homotopy theory, a branch of mathematics, a spectrum is ... category constructed for the purposes of stable homotopy theory, starting with the category of ...
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Category:Homotopy theory
Category:Homotopy theory In algebraic topology, homotopy theory is the study of homotopy groups; and more generally of the ...
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Talk:Spectrum (homotopy theory)
Talk:Spectrum (homotopy theory) With regard to the introduction of spectra ... he first satisfactory construction of the stable homotopy category" in his (I believe) still unpublished ... Lima, The Spanier-Whitehead duality in new homotopy categories. Summa Brasil Math. 4 (1959), 91 ... the category of spectra" or "the stable homotopy category." Adams' construction is described in ...
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Homotopy
Homotopy An illustration of a homotopy between the two bold paths In topology ... other, such a deformation being called a homotopy between the two functions. An outstanding use of homotopy is the definition of homotopy groups and cohomotopy groups, important invariants ...
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Morse theory
Morse theory A Morse function is also an expression ... In differential topology, the techniques of Morse theory give a very direct way of analyzing ... case, reflect the topology quite directly. Morse theory allows one to find CW structures and ... developed some of the ideas of Morse theory in the context of topography. Morse originally applied his theory to geodesics (critical points of the ...
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Nielsen theory
Nielsen theory Nielsen theory is a branch of mathematical research with its origins in topological fixed point theory. Its central ideas were developed by Danish ... Jakob Nielsen, and bear his name. The theory developed in the study of the so ... g) \, | \, g \sim f \}, where ~ indicates homotopy of mappings, and #Fix(g) indicates ...
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Obstruction theory
Obstruction theory In mathematics, obstruction theory is a name for more than one mathematical theory. The older meaning in homotopy theory relates to a procedure, inductive with ...
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Group theory
Group theory Group theory is that branch of mathematics concerned with ... Please refer to the Glossary of group theory for the definitions of terms used throughout group theory. See also list of group theory topics. History There are three historical ...
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Homology theory
Homology theory In mathematics, homology theory is the axiomatic study of the intuitive ... higher. The simplest case is in graph theory, with C and D vertices and homology ... of telescopic cancellation seen in the graph theory case. This explanation is in the style ... orientation and can be used for homology theory. The two boundaries appear as adjoint ...
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