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Alexandroff Homology and Path Homology

Mathematical Notes, 2022
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On homology

Cladistics, 2011
AbstractHomology in cladistics is reviewed. The definition of important terms is explicated in historical context. Homology is not synonymous with synapomorphy: it includes symplesiomorphy, and Hennig clearly included both plesiomorphy and synapomorphy as types of homology.
Kevin C, Nixon, James M, Carpenter
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When is homology not homology?

Current Opinion in Genetics & Development, 1998
Although genes have specific phenotypic consequences in a given species, this functional relationship can clearly change during the course of evolution. Many cases of evolutionary dissociations between homologous genes and homologous morphological features are now known.
G A, Wray, E, Abouheif
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Möbius homology

Transactions of the American Mathematical Society
This paper introduces and develops Möbius homology , a homology theory for representations of finite posets into abelian categories. Although the connection between poset topology and Möbius functions is classical, we go further by establishing a direct connection between poset topology and ...
Amit Patel, Primoz Skraba
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FLOER HOMOLOGY AND INVARIANTS OF HOMOLOGY COBORDISM

International Journal of Mathematics, 1998
By using surgery techniques, we compute Floer homology for certain classes of integral homology 3-spheres homology cobordant to zero. We prove that Floer homology is two-periodic for all these manifolds. Based on this fact, we introduce a new integer valued invariant of integral homology 3-spheres.
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Homological stability for completed homology

Mathematische Annalen, 2015
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Calegari, Frank, Emerton, Matthew
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Homologous Insemination

Fertility and Sterility, 1978
Between July 1, 1969, and October 31, 1977, 619 patients were evaluated for infertility. Homologous insemination (AIH) was employed in 53 patients, many of whom had other contributory causes of infertility. There have been 14 single pregnancies in 11 women, including 4 spontaneous abortions, 1 ectopic pregnancy, 8 term deliveries, and 1 pregnancy in ...
W C, Nunley   +2 more
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From Leibniz Homology to Cyclic Homology

K-Theory, 2002
Given an algebra \(A\), the author constructs a natural homomorphism \(HL_{\ast+1}(A)\to HH_\ast(A)\) from Leibniz to Hochschild homology. If \(f: A\to B\) is a homorphism of algebras, the relative Leibniz homology \(HL_\ast(gl(f))\) is defined and a natural homomorphism \(HL_{\ast+1}(gl(f))\to HC_\ast(F)\) to relative cyclic homology is studied. Thus,
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