6533b85dfe1ef96bd12bdccd
RESEARCH PRODUCT
L 2-topological invariants of 3-manifolds
John LottWolfgang Lücksubject
Discrete mathematicsExact sequenceMathematics::Operator AlgebrasBetti numberGeneral MathematicsMathematics::Spectral TheoryMathematics::Algebraic TopologyManifoldsymbols.namesakeChain (algebraic topology)Von Neumann algebraGromov–Witten invariantsymbolsAlgebraic numberGeometrization conjectureMathematicsdescription
We give results on theL2-Betti numbers and Novikov-Shubin invariants of compact manifolds, especially 3-manifolds. We first study the Betti numbers and Novikov-Shubin invariants of a chain complex of Hilbert modules over a finite von Neumann algebra. We establish inequalities among the Novikov-Shubin invariants of the terms in a short exact sequence of chain complexes. Our algebraic results, along with some analytic results on geometric 3-manifolds, are used to compute theL2-Betti numbers of compact 3-manifolds which satisfy a weak form of the geometrization conjecture, and to compute or estimate their Novikov-Shubin invariants.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1995-12-01 | Inventiones Mathematicae |