On fundamental groups of spaces of framed embeddings of a circle in a 4-manifold

TL;DR

This paper studies the fundamental groups of spaces of framed embeddings of a circle in 4-manifolds, focusing on the case of framed immersed circles, motivated by recent advances in 4-manifold diffeomorphisms.

Contribution

It provides new insights into the fundamental groups of embedding spaces of a circle in 4-manifolds, especially for framed immersed circles, expanding understanding in 4-dimensional topology.

Findings

Analysis of fundamental groups for framed embedding spaces

Results specific to framed immersed circles in 4-manifolds

Connections to recent diffeomorphism results in 4-manifold topology

Abstract

Motivated by recent results on diffeomorphisms of 4-manifolds, this paper investigates fundamental groups of spaces of embeddings of $S^1\times D^3$ in 4-manifolds. The majority of work goes into the case of framed immersed circles.