Survey on L^2-invariants and 3-manifolds

Abstract

In this paper give a survey about L^2-invariants focusing on 3-manifolds.

arXiv comment38 pages. This is the final version and has been accepted for publication in the Bulletin of the London Mathematical Society

References in corpus (28)

• Notes on Perelman's papers
• Criteria for virtual fibering
• The K-theoretic Farrell-Jones Conjecture for hyperbolic groups
• L2-determinant class and approximation of L2-Betti numbers
• Graph manifolds with boundary are virtually special
• L^2-torsion of hyperbolic manifolds of finite volume
• Virtual cubulation of nonpositively curved graph manifolds
• Residually finite rationally solvable groups and virtual fibring
• Twisting $L^2$-invariants with finite-dimensional representations
• The Farrell-Jones conjecture for arbitrary lattices in virtually connected Lie groups
• The Farrell-Jones Conjecture for virtually solvable groups
• Determinant lines, von Neumann algebras and $L^2$ torsion
• Torsion homology growth and cycle complexity of arithmetic manifolds
• The strong Atiyah and Lück approximation conjectures for one-relator groups
• Injectivity radii of hyperbolic integer homology 3-spheres
• Alexander and Thurston norms, and the Bieri-Neumann-Strebel invariants for free-by-cyclic groups
• Mahler measures and Fuglede--Kadison determinants
• The Bieri-Neumann-Strebel invariants via Newton polytopes
• Universal $L^2$-torsion, polytopes and applications to $3$-manifolds
• The action dimension of right-angled Artin groups
• The $L^2$-(co)homology of groups with hierarchies
• Stable integral simplicial volume of 3-manifolds
• $L^2$-Euler characteristics and the Thurston norm
• L2-torsion of hyperbolic manifolds
• Finite-volume hyperbolic 3-manifolds are almost determined by their finite quotient groups
• Localization, Whitehead groups, and the Atiyah Conjecture
• Rational manifold models for duality groups
• The agrarian polytope of two-generator one-relator groups