Structure of semi-continuous $q$-tame persistence modules

@article{Schmahl2020StructureOS,
  title={Structure of semi-continuous \$q\$-tame persistence modules},
  author={Maximilian Schmahl},
  journal={Homology, Homotopy and Applications},
  year={2020}
}
Using a result by Chazal, Crawley-Boevey and de Silva concerning radicals of persistence modules, we show that every lower semi-continuous q-tame persistence module can be decomposed as a direct sum of interval modules and that every upper semi-continuous q-tame persistence module can be decomposed as a product of interval modules. 

Coarse nodal count and topological persistence

Direct generalizations of Courant’s celebrated nodal domain theorem are often false. A notable example is the case of linear combinations of eigenfunc-tions in dimension 2 or more, known as the

PERSISTENCE IN FUNCTIONAL TOPOLOGY AND A CORRECTION TO A THEOREM OF MORSE

During the 1930s, Marston Morse developed a vast generalization of what is commonly known as Morse theory relating the critical points of a semi-continuous functional with the topology of its

Persistent homology for functionals

. We introduce topological conditions on a broad class of functionals that ensure that the persistent homology modules of their associated sublevel set filtration admit persistence diagrams, which, in

Homotopy, homology, and persistent homology using closure spaces and filtered closure spaces

. We develop persistent homology in the setting of filtered (ˇCech) closure spaces. Examples of filtered closure spaces include filtered topological spaces, metric spaces, weighted graphs, and weighted

References

SHOWING 1-10 OF 16 REFERENCES

Rank and Span in Functional Topology

Corrections and Supplementaries to My Paper concerning Krull-Remak-Schmidt’s Theorem

  • G. Azumaya
  • Mathematics
    Nagoya Mathematical Journal
  • 1950
It has recently been found that my previous paper “On generalized semi-primary rings and Krull-Remak-Schmidt’s theorem” Jap. Journ. Math. 19 (1949) — referred to as S. K. — contained in its Theorems

Functional Topology and Abstract Variational Theory.

  • M. Morse
  • Psychology
    Proceedings of the National Academy of Sciences of the United States of America
  • 1938

On the Existence of Minimal Surfaces of General Critical Types.

  • M. MorseC. Tompkins
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1939
It is correct to assert that the completion of each pattern by inclusion of its minor polyedra is uniquely determinate; so that 11 appears to be the total number of systems unlike in respect of numbers and contiguities.

Decomposition of persistence modules

We show that a pointwise finite-dimensional persistence module indexed over a small category decomposes into a direct sum of indecomposables with local endomorphism rings. As an application of this

Éléments de géométrie algébrique

© Publications mathématiques de l’I.H.É.S., 1965, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://

Elements de geometrie algebrique III: Etude cohomologique des faisceaux coherents

© Publications mathématiques de l’I.H.É.S., 1961, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://

Éléments de géométrie algébrique (rédigés avec la collaboration de Jean Dieudonné) : III. Étude cohomologique des faisceaux cohérents, Première partie

L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » ( http://www. ihes.fr/IHES/Publications/Publications.html), implique l’accord avec les conditions générales d’utilisation