homology group

homology group

[hə′mäl·ə·jē ‚grüp]
(mathematics)
Associated to a topological space X, one of a sequence of Abelian groups Hn (X) that reflect how n-dimensional simplicial complexes can be used to fill up X and also help determine the presence of n-dimensional holes appearing in X. Also known as Betti group.
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The 13 selected peer-reviewed papers explore such aspects of logic as an analogy between cardinal characteristics and highness properties of oracles, a non-uniformly C-productive sequence and non-constructive disjunctions, the characterization of the second homology group of stationary type in a stable theory, some questions concerning ab initio generic structures, realizability and existence property of a constructive set theory with types, a goal-directed unbounded coalitional game and its complexity, large cardinals and higher degree theory, and degree spectra of equivalence relations.
It is known from [4] and [7] that in this case the homology group [H.
In this setting, the concept of size function coincides with the dimension of the 0-th multidimensional persistent homology group, i.
and transfer of seven species of the genus Pseudomonas homology group II to the new genus with type species Burkholderia cepacia (Palleroni & Holmes 1981) comb.
2) Compute geometric realizations of a set of generators that form a basis of the first and second homology groups of K (for the zeroth homology group, this is trivial) in O([n.
q](X) is called the qth digital simplicial homology group.
The invariants for two-component handlebody-links are elementary divisors of a matrix whose entries are linking numbers of closed circles corresponding to the basis of one homology group and that of the other homology group.
n-1] on the top homology group of the order complex of [[PI].
In fact, it computes this homotopy group as a homology group of another space (simplicial set): [K.
The modules of this subchain complex are lifts of homology groups [H.
Decomposition theorem for homology groups of symmetric groups.