Graph Cohomology, Colored Posets and Homological Algebra in Functor Categories

• Autorzy: Słomińska J.

Identyfikatory

DOI

10.4064/ba60-3-3

• Języki publikacji: EN

Abstrakty

EN

The homology theory of colored posets, defined by B. Everitt and P. Turner, is generalized. Two graph categories are defined and Khovanov type graph cohomology are interpreted as Ext* groups in functor categories associated to these categories. The connection, described by J. H. Przytycki, between the Hochschild homology of an algebra and the graph cohomology, defined for the same algebra and a cyclic graph, is explained from the point of view of homological algebra in functor categories.

Słowa kluczowe

EN

functor categories; graph categories; graph cohomology

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2012
• Tom: Vol. 60, no 3
• Strony: 219--239
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Słomińska J.

• Faculty of Mathematics and Information Sciences Warsaw University of Technology Plac Politechniki 1 00-661 Warszawa, Poland

Bibliografia

• [1] G. Carlsson, Derived completions in stable homotopy theory, J. Pure Appl. Algebra 212 (2008), 550–577.
• [2] B. Everitt and P. Turner, Homology of coloured posets: a generalization of Khovanov’s cube construction, J. Algebra 322 (2009), 429–448.
• [3] L. Helme-Guizon and Y. W. Rong, Graph cohomologies from arbitrary algebras, arXiv:math/0506023.
• [4] L. Helme-Guizon, J. H. Przytycki and Y. W. Rong, Torsion in graph homology, Fund. Math. 190 (2006), 139–177.
• [5] M. Khovanov, A categorification of the Jones polynomial, Duke Math. J. 101 (2000), 359–426.
• [6] J.-L. Loday, Cyclic Homology, Grundlehren Math. Wiss. 301, Springer, 1992.
• [7] J. P. May, Simplicial Objects in Algebraic Topology, Van Nostrand, Princeton, 1967.
• [8] D. Notbohm and N. Ray, On Davis–Januszkiewicz homotopy types I; formality and rationalisation, Algebr. Geom. Topol. 5 (2005), 31–51.
• [9] J. H. Przytycki, When the theories meet: Khovanov homology as Hochschild homology of links, Quantum Topol. 1 (2010), 93–109.
• [10] C. A.Weibel, An Introduction to Homological Algebra, Cambridge Univ. Press, 1994.
• [11] M. Zimmermann, Complexes de chaînes et petites catégories, www-irma.u-strasbg. fr/annexes/publications/pdf/04020.pdf.