𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Rational Betti numbers of configuration spaces

✍ Scribed by Yves Félix; Jean-Claude Thomas

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
105 KB
Volume
102
Category
Article
ISSN
0166-8641

No coin nor oath required. For personal study only.

✦ Synopsis

We compute the rational Betti numbers of the configuration space C k (M) of k points in an evendimensional orientable closed manifold M and prove that these numbers depend only on the rational cohomology algebra of the manifold. We give also a formula for the Euler-Poincaré characteristic of C k (M) in terms only of k, and of the Euler-Poincaré characteristic of M.

📜 SIMILAR VOLUMES

Sequences of Betti numbers
Sequences of Betti numbers
✍ Mark Ramras 📂 Article 📅 1980 🏛 Elsevier Science 🌐 English ⚖ 575 KB
Exponential growth of Betti numbers
Exponential growth of Betti numbers
✍ Irena Peeva 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 430 KB

We prove over some local commutative noetherian rings that the sequence of Betti numbers of every finitely generated module is either eventually constant or has termwise exponential growth.