Cohomology of spaces of complex knots

TL;DR

This paper introduces a new technique for calculating the cohomology groups of spaces of complex parametric knots in complex Euclidean spaces, providing explicit results for low-dimensional groups.

Contribution

The authors develop a novel method for computing cohomology of complex knot spaces and perform explicit calculations for low-dimensional cases.

Findings

Successfully calculated low-dimensional cohomology groups

Developed a new computational technique for complex knot spaces

Provided explicit examples of cohomology groups

Abstract

We develop a technique for calculating the cohomology groups of spaces of complex parametric knots in ${\mathbb C}^k$, $k \geq 3$, and carry out these calculations to obtain these groups of low dimensions.