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This technical report introduces a novel approach to efficient computation in homological algebra over fields, with particular emphasis on computing the persistent homology of a filtered topological cell complex.
Matroid Decomposition
Truemper, K · 1992
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Oriented Matroids
Björner, A., Vergnas, M. L., Sturmfels, B., White, N., and Ziegler, G. M · 1993
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Morse theory for cell complexes
Forman, R · 1998
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Combinatorial Optimization: Algorithms and Complexity
Papdimitriou, C., and Steiglitz, K · 1998
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Discrete Morse theory for free chain complexes
Kozlov, D · 2005
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Computing persistent homology
Zomorodian, A., and Carlsson, G · 2005
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Sköldberg, E · 2006
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Shareshian, J., and Wachs, M · 2007
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Kozlov, D · 2008
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Carlsson, G · 2009
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Bauer, U · 2011
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Oxley, J · 2011
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Curry, J., Ghrist, R., and Nanda, V · 2013
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Distributed computation of persistent homology
Bauer, U., Kerber, M., and Reininghaus, J · 2014
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Elementary Applied Topology
Ghrist, R · 2014
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Robinson, M · 2014
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https://plot.ly , 2015
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Clique topology reveals intrinsic geometric structure in neural correlations
Giusti, C., Pastalkova, E., Curto, C., and Itskov, V · 2015
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Persistence Theory: From Quiver Representations to Data Analysis
Oudot · 2015
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Eirene: a platform for computational homological algebra
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Discrete Morse theory and classifying spaces
Nanda, V., Tamaki, D., and Tanaka, K · 2013
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A roadmap for the computation of persistent homology
Otter, N., Porter, M. A., Tillmann, U., Grindrod, P., and Harrington, H. A
Cited in the paper.
Henselman, G · 2016
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Matroids, Filtrations, and Applications
Henselman, G · 2016
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