Results 11 to 20 of about 1,026,270 (282)
Journal of High Energy Physics, 2006 D-branes are classified by twisted K-theory. Yet twisted K-theory is often hard to calculate. We argue that, in the case of a compactification on a simply-connected six manifold, twisted K-theory is isomorphic to a much simpler object, twisted homology ...
Collinucci, Andres, Evslin, Jarah
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Andr\'e-Quillen homology via functor homology [PDF]
Proceedings of the American Mathematical Society, 2001 We obtain Andr\'e-Quillen homology for commutative algebras using relative homological algebra in the category of functors on finite pointed ...
Pirashvili, Teimuraz
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Homological scaffold via minimal homology bases [PDF]
Scientific Reports, 2021 AbstractThe homological scaffold leverages persistent homology to construct a topologically sound summary of a weighted network. However, its crucial dependency on the choice of representative cycles hinders the ability to trace back global features onto individual network components, unless one provides a principled way to make such a choice.
Guerra, Marco +4 more
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Homology of homologous knotted proteins
Journal of The Royal Society Interface, 2023 Quantification and classification of protein structures, such as knotted proteins, often requires noise-free and complete data. Here, we develop a mathematical pipeline that systematically analyses protein structures. We showcase this geometric framework on proteins forming open-ended trefoil knots, and we demonstrate that the mathematical tool ...
Katherine Benjamin +6 more
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Homology, Homotopy and Applications, 2017 12 pages; revised version incorporates suggestions from referee.
Nelson, Sam, Rosenfield, Jake
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Magnitude homology and path homology
Bulletin of the London Mathematical Society, 2022 version 3 (refined some proofs, added some figures, and fixed some typos. To appear in Bulletin of the London Mathematical Society)
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Canadian Journal of Mathematics, 2003 AbstractFor complex projective manifolds we introduce polar homology groups, which are holomorphic analogues of the homology groups in topology. The polar k-chains are subvarieties of complex dimension k with meromorphic forms on them, while the boundary operator is defined by taking the polar divisor and the Poincaré residue on it. One can also define
Khesin, B., Rosly, A.
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Rabinowitz Floer homology and symplectic homology [PDF]
, 2009 The Rabinowitz-Floer homology groups $RFH_*(M,W)$ are associated to an exact embedding of a contact manifold $(M,\xi)$ into a symplectic manifold $(W,\omega)$. They depend only on the bounded component $V$ of $W\setminus M$.
Cieliebak, Kai +2 more
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Leibniz homology of Lie algebras as functor homology [PDF]
, 2014 We prove that Leibniz homology of Lie algebras can be described as functor homology in the category of linear functors from a category associated to the Lie operad.Comment: 26 ...
Hoffbeck, Eric, Vespa, Christine
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Digital homotopy relations and digital homology theories
Applied General Topology, 2021 In this paper we prove results relating to two homotopy relations and four homology theories developed in the topology of digital images. We introduce a new type of homotopy relation for digitally continuous functions which we call ``strong homotopy ...
P. Christopher Staecker
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