Chain complex and Homotopy

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Chain complex and Homotopy

Chain complex vs. Homotopy

In mathematics, a chain complex is an algebraic structure that consists of a sequence of abelian groups (or modules) and a sequence of homomorphisms between consecutive groups such that the image of each homomorphism is included in the kernel of the next. In topology, two continuous functions from one topological space to another are called homotopic (from Greek ὁμός homós "same, similar" and τόπος tópos "place") if one can be "continuously deformed" into the other, such a deformation being called a homotopy between the two functions.

Similarities between Chain complex and Homotopy

Chain complex and Homotopy have 5 things in common (in Unionpedia): Algebraic topology, Equivalence relation, Group homomorphism, Homology (mathematics), Topological space.

Algebraic topology

Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces.

Algebraic topology and Chain complex · Algebraic topology and Homotopy · See more »

Equivalence relation

In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive.

Chain complex and Equivalence relation · Equivalence relation and Homotopy · See more »

Group homomorphism

In mathematics, given two groups, (G, ∗) and (H, ·), a group homomorphism from (G, ∗) to (H, ·) is a function h: G → H such that for all u and v in G it holds that where the group operation on the left hand side of the equation is that of G and on the right hand side that of H. From this property, one can deduce that h maps the identity element eG of G to the identity element eH of H, and it also maps inverses to inverses in the sense that Hence one can say that h "is compatible with the group structure".

Chain complex and Group homomorphism · Group homomorphism and Homotopy · See more »

Homology (mathematics)

In mathematics, homology is a general way of associating a sequence of algebraic objects such as abelian groups or modules to other mathematical objects such as topological spaces.

Chain complex and Homology (mathematics) · Homology (mathematics) and Homotopy · See more »

Topological space

In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods.

Chain complex and Topological space · Homotopy and Topological space · See more »

The list above answers the following questions

What Chain complex and Homotopy have in common
What are the similarities between Chain complex and Homotopy

Chain complex and Homotopy Comparison

Chain complex has 48 relations, while Homotopy has 81. As they have in common 5, the Jaccard index is 3.88% = 5 / (48 + 81).

References

This article shows the relationship between Chain complex and Homotopy. To access each article from which the information was extracted, please visit:

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