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searching for Relative homology 7 found (25 total)

Fundamental class (658 words) [view diff] exact match in snippet view article find links to article

If M is a compact orientable manifold with boundary, then the top relative homology group is again infinite cyclic H n ( M , ∂ M ) ≅ Z {\displaystyle

Hurewicz theorem (1,309 words) [view diff] exact match in snippet view article find links to article

h_{*}\colon \pi _{k}(X,A)\to H_{k}(X,A)} from relative homotopy groups to relative homology groups. The Relative Hurewicz Theorem states that if both X {\displaystyle

Burau representation (1,525 words) [view diff] exact match in snippet view article find links to article

marked points. Then instead of considering H1(Cn) one considers the relative homology H1(Cn, Γ) where γ ⊂ Dn is the part of the boundary of Dn corresponding

Barycentric subdivision (2,530 words) [view diff] exact match in snippet view article find links to article

to compare the homology groups. Excision can be used to determine relative homology groups. It allows in certain cases to forget about subsets of topological

Algebraic K-theory (10,382 words) [view diff] exact match in snippet view article find links to article

and K1 could be fit together into an exact sequence similar to the relative homology exact sequence. Work in K-theory from this period culminated in Bass'

Topological recursion (4,377 words) [view diff] exact match in snippet view article find links to article

\mathbf {d} =(d_{1},\dots ,d_{b_{2}({\mathfrak {X}})})} is the 2nd relative homology class of the surface's image, and μ i ∈ H 1 ( L , Z ) {\displaystyle

Topological data analysis (11,259 words) [view diff] exact match in snippet view article find links to article

other basic concepts in algebraic topology, such as cohomology and relative homology/cohomology. An interesting application is the computation of circular