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Natural Homology [chapter]

Jérémy Dubut, Éric Goubault, Jean Goubault-Larrecq
2015 Lecture Notes in Computer Science  
We propose a notion of homology for directed algebraic topology, based on so-called natural systems of abelian groups, and which we call natural homology.  ...  Natural Homology of Pospaces, and Natural Systems Let X be a pospace, i.e., a topological space X with a partial order ≤ whose graph is closed in X 2 .  ...  In particular, it has non-trivial natural homology, in the strong sense that its natural homology is not bisimilar to any natural system consisting only of copies of Z (e.g., the natural homology of a  ... 
doi:10.1007/978-3-662-47666-6_14 fatcat:wg5s76lqx5ekrhqaogpnww6qly

The Homological Nature of Entropy

Pierre Baudot, Daniel Bennequin
2015 Entropy  
We propose that entropy is a universal co-homological class in a theory associated to a family of observable quantities and a family of probability distributions.  ...  In the second part we give the complete definitions and proofs of the theorems A, C and E in the introduction, which show why entropy is the first homological invariant of a structure of information in  ...  The invariant co-homology is probably a more natural object from the point of view of Physics. It is also on this co-homology that we were able to obtain constructive results.  ... 
doi:10.3390/e17053253 fatcat:klalgwiiyvadtgbstslyearvpe

Natural homologs of gramicidin S

1984 Journal of antibiotics (Tokyo. 1968)  
NATURAL HOMOLOGS OF GRAMICIDIN S Sir: As natural gramicidin S only a single compound, cyclo(Val-Orn-Leu-D-Phe-Pro)2, is known, although peptide antibiotics produced by microorganisms usually consist of  ...  Isolation of the homologous peptides showed that the well-known antibiotic, gramicidin S, is a member of a "family" as other antibiotics') yielded by B. brevis.  ... 
doi:10.7164/antibiotics.37.689 fatcat:xvelvryyg5dxfn73n63sugeqv4

Natural symmetries of secondary Hochschild homology [article]

David Ayala, John Francis, Adam Howard
2021 arXiv   pre-print
We show that the group of framed diffeomorphisms of the torus acts on twice-iterated Hochschild homology, and explain how this recovers a host of familiar symmetries.  ...  Based on this, we propose a definition of an unstable secondary cyclotomic structure, and show that iterated Hochschild homology possesses such in the Cartesian monoidal setting.  ...  Natural symmetries of secondary Hochschild homology Conventions.  ... 
arXiv:2111.08798v2 fatcat:2ajrg2a4evgytjfv622s75b4iq

Projective Naturality in Heegaard Floer Homology [article]

Mike Gartner
2019 arXiv   pre-print
We discuss an application to involutive Heegaard Floer homology, and potential generalizations of our results.  ...  Juhász, Thurston and Zemke showed that the Heegaard Floer invariants are natural with respect to diffeomorphisms, in the sense that there are functors HF^∘: Man_*→F_2[U]-Mod whose values agree with the  ...  Here H(D) ∈ H 2 (Y ; Z) is the homology class naturally associated to the periodic domain D.  ... 
arXiv:1908.06237v1 fatcat:ypyexjmf5rf6lb4d76oko334ea

Naturality in sutured monopole and instanton homology

John A. Baldwin, Steven Sivek
2015 Journal of differential geometry  
Kronheimer and Mrowka defined invariants of balanced sutured manifolds using monopole and instanton Floer homology.  ...  The functors SHI g and SHI g from DiffSut g to C-PSys are naturally isomorphic. q.e.d. Instanton Knot Homology.  ...  Below, we discuss some applications of these "naturality" results, mostly in the context of twisted sutured monopole homology.  ... 
doi:10.4310/jdg/1432842360 fatcat:dvg7lyo775erjpjbl4qjhifiju

Natural transformations from constructible functions to homology [article]

Gary Kennedy, Clint McCrory, Shoji Yokura
1994 arXiv   pre-print
For complex projective varieties, all natural transformations from constructible functions to homology (modulo torsion) are linear combinations of the MacPherson-Schwartz-Chern classes.  ...  If σ(1 Z ) is zero in the homology group of Z, then by naturality it is likewise zero in the homology group of X.  ...  Then each individual component c i of the Chern class natural transformation (assigning to the characteristic function 1 X of a nonsingular variety the homology class c i (T X) ⌢ [X]) is likewise a natural  ... 
arXiv:alg-geom/9407008v1 fatcat:hfb6hi3rd5fa5mesdwfnu2vugi

Naturality and mapping class groups in Heegaard Floer homology [article]

András Juhász, Dylan P. Thurston, Ian Zemke
2018 arXiv   pre-print
We show that all versions of Heegaard Floer homology, link Floer homology, and sutured Floer homology are natural.  ...  In fact, this allows us to give sufficient conditions for an arbitrary invariant of multi-pointed Heegaard diagrams to descend to a natural invariant of 3-manifolds, links, or sutured manifolds.  ...  Here, we do not use naturality, only that Heegaard Floer homology is well-defined up to isomorphism in each Spin c structure and relative homological grading, as shown by Ozsváth and Szabó [27] .  ... 
arXiv:1210.4996v4 fatcat:hfas2oq4qrcepafemsdz2a7fcy

Symplectic Instanton Homology: naturality, and maps from cobordisms [article]

Guillem Cazassus
2019 arXiv   pre-print
We prove that Manolescu and Woodward's Symplectic Instanton homology, and its twisted versions are natural, and define maps associated to four dimensional cobordisms within this theory.  ...  representations of the mapping class group and the fundamental group of a 3-manifold, and to have a geometric interpretation of the maps appearing in the long exact sequence for symplectic instanton homology  ...  Independence of the decomposition, naturality.  ... 
arXiv:1710.03872v2 fatcat:bg5eiyk35rftxi2yi6tyw36a34

Debatable homologies

Diethard Tautz
1998 Nature  
*Homology, Novartis Foundation, London, 21-23 July 1998. Proceedings to be published by Wiley. Nature © Macmillan Publishers Ltd 1998  ...  Owen's original concept of homology did not have a phylogenetic (evolutionary) perspective. It was based on the philosophy of identifying and grouping similarities in nature, the 'scala naturae' .  ... 
doi:10.1038/25604 pmid:9738490 fatcat:xl4nq4y4wnhf5da67qvqipxr34

Lifespan Functors and Natural Dualities in Persistent Homology [article]

Ulrich Bauer, Maximilian Schmahl
2021 arXiv   pre-print
They also naturally appear in duality results for absolute and relative versions of persistent (co)homology, generalizing previous results in terms of barcodes.  ...  Due to their functoriality, we can apply these results to morphisms in persistent homology that are induced by morphisms between filtrations.  ...  Here, naturality is inherited from the construction of the long exact homology sequence.  ... 
arXiv:2012.12881v3 fatcat:y6cz2wonybclhgtku6u5gxpkme

Natural reservoirs for homologs of hepatitis C virus

Stephanie Pfaender, Richard JP Brown, Thomas Pietschmann, Eike Steinmann
2014 Emerging Microbes and Infections  
Hepatitis C virus displays a narrow host species tropism, naturally infecting only humans, although chimpanzees are also susceptible to experimental infection.  ...  Rodents/bats The discovery of closely related hepaciviral homologs of HCV, which naturally infect equine hosts, raised the possibility that additional Table 2 ).  ...  Indeed, the group of Quan and colleagues 15 identified bats as a major natural reservoir for hepaciviruses and pegiviruses.  ... 
doi:10.1038/emi.2014.19 pmid:26038514 pmcid:PMC3974340 fatcat:ap2qrihmobfirmee7dr227v5vy

Phosphotransferase sequence homology

1987 Nature  
The homologies were found in the course of developing a programming system for the analysis of sequence patterns.  ...  SIR-I wish to report a remarkable sequence homology which is found in a number of different enzymes all of which confer antibiotic resistance by acting as phosphotransferases.  ... 
doi:10.1038/329021a0 pmid:3041224 fatcat:uxovaggchfa4rghapopdvc37va

Plumbing is a natural operation in Khovanov homology [article]

Thomas Kindred
2017 arXiv   pre-print
We apply this plumbing of chains to to prove that every homogeneously adequate state has enhancements X^± in distinct j-gradings whose A-traces (which we define) represent nonzero Khovanov homology classes  ...  nonzero homology classes.  ...  What do (representatives of) nonzero Khovanov homology classes look like?  ... 
arXiv:1705.01931v1 fatcat:hnrohbcg7neo7h7orhdhethnvy

On the Naturality of the Spectral Sequence from Khovanov Homology to Heegaard Floer Homology

J. E. Grigsby, S. M. Wehrli
2010 International mathematics research notices  
homology for sutured manifolds developed by Juhász in [7] .  ...  In the present work we prove the naturality of the spectral sequence under certain elementary TQFT operations, using a generalization of Juhász's surface decomposition theorem valid for decomposing surfaces  ...  We recall it here, since it provides another example of the naturality of the spectral sequence relating Khovanov homology and Heegaard Floer homology.  ... 
doi:10.1093/imrn/rnq039 fatcat:ixaypptjmnderlkae3i25vnsse
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