NEW BOUNDS ON THE BETTI NUMBERS OF NILPOTENT LIE-ALGEBRAS

Authors
CAIRNS G JESSUP B
Citation
G. Cairns et B. Jessup, NEW BOUNDS ON THE BETTI NUMBERS OF NILPOTENT LIE-ALGEBRAS, Communications in algebra, 25(2), 1997, pp. 415-430
Citations number
13
Categorie Soggetti
Mathematics, Pure",Mathematics
Journal title
Communications in algebra → ACNP
ISSN journal
00927872
Volume
25
Issue
2
Year of publication
1997
Pages
415 - 430
Database
ISI
SICI code
0092-7872(1997)25:2<415:NBOTBN>2.0.ZU;2-1
Abstract
We provide new upper and lower bounds for the Betti numbers of nilpote nt Lie algebras. As an application, we prove the toral rank conjecture (TRC) for nilmanifolds of dimension at most 14 and for a small class of coformal spaces. We also give a new, direct proof of the result of Deninger and Singhof that the TRC is true for a-step nilpotent Lie alg ebras.