A Non-classification Result for Wild Knots

TL;DR

This paper demonstrates that classifying wild knots is fundamentally more complex than classifying countable structures, using descriptive theory methods to establish the increased difficulty.

Contribution

It introduces a non-classification result showing the greater complexity of wild knots compared to countable structures.

Findings

Wild knots classification is strictly harder than countable structures

Descriptive theory methods are effective in analyzing knot complexity

The result clarifies the hierarchy of classification problems in topology

Abstract

Using methods of descriptive theory it is shown that the classification problem for wild knots is strictly harder than that for countable structures.