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.
References in periodicals archive ?
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.
n-1] on the top homology group of the order complex of [[PI].
In the graph case the coefficients of these basis vectors are [+ or -] 1; in the general case, they are (up to sign) the cardinalities of homology groups of cellular spanning trees obtained from T by matroid basis exchange.
The book begins with a review of smooth manifolds, and then covers topics including stratifolds and stratifolds with boundaries, Z/2-homology, the Mayer-Vietoris sequence and homology groups of spheres, and Brouwer's fixed point theorem.
In the patent space we introduce new features for drawing and searching Markush structures, including support for homology groups and repeating units.
Accelrys Direct also integrates enhancements derived from the Accelrys Pipeline Pilot and Accord cartridges to enhance scalability while offering improved capabilities in handling Markush homology groups.
It surveys several algebraic invariants: the fundamental group, singular and Cech homology groups, and a variety of cohomology groups.
Blackburn:1972] Blackburn Norman, 1972, Some homology groups of wreathe products, Illinois J.
He provides all the necessary prerequisites for graduate students and practitioners, describing Riemann surfaces (including coverings, analytical continuation, and Puiseaux expansion), holomorphic functions of several variables (including analytic sets and analytic set germs as well as regular and singular points of analytic sets), isolated singularities of holomorphic functions (including isolated critical points and the universal unfolding), fundamentals of differential topology (including singular homology groups and linking numbers), and the topology of singularities (including the Picard-Lefschetz theorem, the Milnor fibration, the Coxeter-Dynkin diagram, the Selfert form and the action of the braid group.