𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Finiteness of rank invariants of multidimensional persistent homology groups

✍ Scribed by Francesca Cagliari; Claudia Landi

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
199 KB
Volume
24
Category
Article
ISSN
0893-9659

No coin nor oath required. For personal study only.

✦ Synopsis

Rank invariants of multidimensional persistent homology groups are a parameterized version of Betti numbers of a space multi-filtered by a continuous vector-valued function.

In this note we give a sufficient condition for their finiteness. This condition is sharp for spaces embeddable in R n .

📜 SIMILAR VOLUMES

Cohomological Invariants of Simply Conne
Cohomological Invariants of Simply Connected Groups of Rank 3
✍ Alexander Merkurjev 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 152 KB

Let G be a linear algebraic group defined over a field F. One can define an equivalence relation (called R-equivalence) on the group G F of points over F as follows (cf. [4, 9, 14]). Two points g 0 g 1 ∈ G F are R-equivalent, if there is a rational morphism f 1 F → G of algebraic varieties over F de

Locally (Soluble-by-Finite) Groups of Fi
Locally (Soluble-by-Finite) Groups of Finite Rank
✍ Martyn R. Dixon; Martin J. Evans; Howard Smith 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 178 KB

But P l B s rad P and so L ( Prrad P. It remains to show that P F L . 1 2 If Q is a maximal normal subgroup of P then, since P is perfect, PrQ is isomorphic to a simple direct factor of L and hence has order greater 1 than s. With the notation as in Lemma 2.2, we have PE rE ( PrP l E , 2 2 2 which t

Semi-invariants of Finite Reflection Gro
Semi-invariants of Finite Reflection Groups
✍ Anne V Shepler 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 99 KB

Let G be a finite group of complex n = n unitary matrices generated by reflections acting on ‫ރ‬ n . Let R be the ring of invariant polynomials, and let be a multiplicative character of G. Let ⍀ be the R-module of -invariant differential forms. We define a multiplication in ⍀ and show that under thi