Homology theory
Homology theory In mathematics, homology theory is the axiomatic study of the intuitive geometric idea of homology of cycles on topological spaces. It ...
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Category:Homology theory
Category:Homology theory In mathematics, homology theory is the axiomatic study of the intuitive geometric idea of homology of cycles on topological spaces. It ...
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Talk:Homology theory
Talk:Homology theory At the intuitive level homology is taken to be an equivalence relation ... the intuitive, geometric motivation. It is how homology was first conceived. The formal definition is ... is why we're trying to define "homology" as in "these two curves are ...
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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 ... and to obtain substantial information about their homology. Before Morse, Arthur Cayley and James Clerk ... developed some of the ideas of Morse theory in the context of topography. Morse ...
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Floer homology
Floer homology In mathematics, Floer homology refers to a family of homology theories which share similar characteristics and are ... work. They are all modelled upon Morse homology on finite-dimensional manifolds, extending it to ... three-manifolds all yield three types of homology groups, that fit into an exact ...
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Morse homology
Morse homology In mathematics, specifically in the field of differential topology, Morse homology is a homology theory defined for any smooth manifold. It is ... and is in fact isomorphic to singular homology. Morse homology also serves as a ...
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Category theory
Category theory In mathematics, category theory deals in an abstract way with mathematical ... with algebraic topology. See list of category theory topics for a breakdown of relevant articles ... as mathematical theories have traditionally done, category theory emphasizes the morphisms — the structure-preserving ... an important part of the transition from homology (an intuitive and geometric concept) to ...
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Homology (mathematics)
Homology (mathematics) In mathematics (especially algebraic topology and abstract algebra), homology (in Greek homos = identical) is a certain ... a topological space or a group). See homology theory for more background. For a topological space, the homology groups are generally much easier to ...
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Khovanov homology
Khovanov homology In mathematics, Khovanov homology is a homology theory for knots and links. It may be ... number of right-handed crossings. The Khovanov homology of L is then defined as ...
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Chromosome theory   (translated from Japanese)
Chromosome theory Chromosome theoryThe せ which (the plug it ... does and the ょ く wants, Chromosome theory (of inheritance), same: Chromosome theory) with, heredity chromosome . As for this theory gene is on the chromosome, with present ... do not follow this. As for chromosome theory バッタ was used cytology observationWalter S ...
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