Cheeger-Gromov L 2 -invariants of 3-manifolds Geunho Lim Indiana - - PowerPoint PPT Presentation

Cheeger-Gromov L2 ρ-invariants

• f 3-manifolds

Geunho Lim Indiana University Bloomington limg@iu.edu

L2 ρ-invariants

• Topological Definition of L2 ρ-invariants, ρ (2)(M,φ)

M is a closed (4k-1)-manifold. φ: π 1(M) → G is a homomorphism. Suppose there are a 4k-manifold W such that ∂W = M and a group Γ which make the following diagram commute: Then,

Topological approach to L2 ρ-invariants

• Theorem [Cha 16]

For a closed 3-manifold M with simplicial complexity n, |ρ (2)(M,φ)| ≤ 363090n for any homomorphism φ: π 1(M) → G.

• Theorem [L, work in progress]

For a spherical 3-manifold M with simplicial complexity n, |ρ (2)(M,φ)| ≤ 2340n for any homomorphism φ: π 1(M) → G.