O-Minimal Spectra, Infinitesimal Subgroups and Cohomology

Journal of Symbolic Logic 72 (4):1177 - 1193 (2007)

By recent work on some conjectures of Pillay, each definably compact group G in a saturated o-minimal expansion of an ordered field has a normal "infinitesimal subgroup" G00 such that the quotient G/G00, equipped with the "logic topology", is a compact (real) Lie group. Our first result is that the functor G → G/G00 sends exact sequences of definably compact groups into exact sequences of Lie groups. We then study the connections between the Lie group G/G00 and the o-minimal spectrum G̃ of G. We prove that G/G00 is a topological quotient of G̃. We thus obtain a natural homomorphism ψ* from the cohomology of G/G00 to the (Čech-)cohomology of G̃. We show that if G00 satisfies a suitable contractibility conjecture then $\widetilde{G^{00}}$ is acyclic in Čech cohomology and ψ* is an isomorphism. Finally we prove the conjecture in some special cases
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2178/jsl/1203350779
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 39,545
Through your library

References found in this work BETA

Type-Definability, Compact Lie Groups, and o-Minimality.Anand Pillay - 2004 - Journal of Mathematical Logic 4 (02):147-162.
Definably Compact Abelian Groups.Mário J. Edmundo & Margarita Otero - 2004 - Journal of Mathematical Logic 4 (02):163-180.
Intersection Theory for o-Minimal Manifolds.Alessandro Berarducci & Margarita Otero - 2001 - Annals of Pure and Applied Logic 107 (1-3):87-119.
A Remark on Divisibility of Definable Groups.Mário J. Edmundo - 2005 - Mathematical Logic Quarterly 51 (6):639-641.

View all 7 references / Add more references

Citations of this work BETA

Connected Components of Definable Groups, and o-Minimality II.Annalisa Conversano & Anand Pillay - 2015 - Annals of Pure and Applied Logic 166 (7-8):836-849.

Add more citations

Similar books and articles

Jack and Jill Have Shifted Spectra.Ned Block - 1999 - Behavioral and Brain Sciences 22 (6):946-947.
Bad Groups of Finite Morley Rank.Luis Jaime Corredor - 1989 - Journal of Symbolic Logic 54 (3):768-773.
Spectra of Formulae with Henkin Quantifiers.Joanna Golinska-Pilarek & Konrad Zdanowski - 2003 - In A. Rojszczak, J. Cachro & G. Kurczewski (eds.), Philosophical Dimensions of Logic and Science. Kluwer Academic Publishers.
Transfer Methods for o-Minimal Topology.Alessandro Berarducci & Margarita Otero - 2003 - Journal of Symbolic Logic 68 (3):785-794.
Generix Never Gives Up.Eric Jaligot - 2006 - Journal of Symbolic Logic 71 (2):599 - 610.
Maharam Spectra of Loeb Spaces.Renling Jin & H. Jerome Keisler - 2000 - Journal of Symbolic Logic 65 (2):550-566.
A Hyperimmune Minimal Degree and an ANR 2-Minimal Degree.Mingzhong Cai - 2010 - Notre Dame Journal of Formal Logic 51 (4):443-455.


Added to PP index

Total views
19 ( #397,744 of 2,325,427 )

Recent downloads (6 months)
9 ( #140,153 of 2,325,427 )

How can I increase my downloads?


My notes

Sign in to use this feature