Spectral Sequences, Exact Couples and Persistent Homology of filtrations

@article{Basu2013SpectralSE,
  title={Spectral Sequences, Exact Couples and Persistent Homology of filtrations},
  author={Saugata Basu and Laxmi Parida},
  journal={CoRR},
  year={2013},
  volume={abs/1308.0801}
}
In this paper we study the relationship between a very classical algebraic object associated to a filtration of topological spaces, namely a spectral sequence introduced by Leray in the 1940’s, and a more recently invented object that has found many applications – namely, its persistent homology groups. We show the existence of a long exact sequence of groups linking these two objects and using it derive formulas expressing the dimensions of each individual groups of one object in terms of the… CONTINUE READING
Recent Discussions
This paper has been referenced on Twitter 4 times over the past 90 days. VIEW TWEETS

From This Paper

Topics from this paper.

Citations

Publications citing this paper.

References

Publications referenced by this paper.
Showing 1-10 of 19 references

Computational topology, American Mathematical Society, Providence, RI, 2010, An introduction

  • Herbert Edelsbrunner, John L. Harer
  • MR 2572029 (2011e:00001) 2,
  • 2011
Highly Influential
9 Excerpts

Exact couples in algebraic topology

  • W. S. Massey
  • 1952
Highly Influential
5 Excerpts

Structure de l’anneau d’homologie d’une représentation

  • Jean Leray
  • C. R. Acad. Sci. Paris
  • 1946
Highly Influential
3 Excerpts

and F

  • A. Romero, J. Heras, G. Mata, J. Rubio
  • Sergeraert, Spectral sequences for computing…
  • 2013
2 Excerpts

West Lafayette, IN 47906, U.S.A. E-mail address: sbasu@math.purdue.edu URL: www.math.purdue.edu/~sbasu Computational Genomics

  • Shmuel Weinberger
  • .persistent homology?, Notices Amer. Math. Soc
  • 2011
3 Excerpts

, and Raimund Seidel . On the shape of a set of points in the plane

  • Herbert Edelsbrunner, David G. Kirkpatrick
  • Harer . Computational topology
  • 2010

A history of algebraic and differential topology 1900–1960

  • Jean Dieudonné
  • Modern Birkhäuser Classics, Birkhäuser Boston…
  • 2009

Éléments de mathématique

  • N. Bourbaki
  • Algèbre. Chapitre 10. Algèbre homologique…
  • 2007

Similar Papers

Loading similar papers…