Exact values of complexity for Paoluzzi - Zimmermann manifolds

TL;DR

This paper determines the exact Matveev complexity values and calculates epsilon-invariants for a specific family of hyperbolic 3-manifolds with boundary, advancing understanding of their topological complexity.

Contribution

It provides the first exact complexity values and epsilon-invariants for the Paoluzzi-Zimmermann manifolds, a significant step in classifying hyperbolic 3-manifolds.

Findings

Exact complexity values for the manifolds are established.

Epsilon-invariants for these manifolds are computed.

Results enhance the classification of hyperbolic 3-manifolds.

Abstract

There are found exact values of (Matveev) complexity for the 2-parameter family of hyperbolic 3-manifolds with boundary constructed by Paoluzzi and Zimmermann. Moreover, $\epsilon$-invariants for these manifolds are calculated.