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

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.

21 pages, 1 figure. v2: Fixed some typos. v3: Simplified some proofs, and removed the part concerning nonframed cases as it contained an error. This is possible to fix, but will appear in another paper. v4: published version

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