Replacing a graph clasper by tree claspers

TL;DR

This paper demonstrates that surgeries along connected, strict graph claspers of degree n can be replaced by sequences of surgeries along strict tree claspers of the same degree, simplifying the analysis of link equivalences.

Contribution

It establishes that graph clasper surgeries can be systematically replaced by tree clasper surgeries, providing a new method for understanding link transformations.

Findings

Graph clasper surgeries are equivalent to sequences of tree clasper surgeries.

Simplifies the process of analyzing link equivalences.

Provides a new approach for studying link invariants.

Abstract

We prove that two links related by a surgery along a connected, strict graph clasper of degree n are C_n-equivalent, i.e, related by a sequence of surgeries along strict tree claspers of degree n.