Theta-graph and diffeomorphisms of some 4-manifolds

Abstract

In this article, we construct countably many mutually non-isotopic diffeomorphisms of some closed non simply-connected 4-manifolds that are homotopic to but not isotopic to the identity, by surgery along $\Theta$-graphs. As corollaries of this, we obtain some new results on codimension 1 embeddings and pseudo-isotopies of 4-manifolds. In the proof of the non-triviality of the diffeomorphisms, we utilize a twisted analogue of Kontsevich's characteristic class for smooth bundles, which is obtained by extending a higher dimensional analogue of Marché--Lescop's "equivariant triple intersection" in configuration spaces of 3-manifolds to allow Lie algebraic local coefficient system.

arXiv comment62 pages, 14 figures, v4: slightly simplified (restricted to even dimensions, omitted proof of Proposition 6.5), expanded explanations about products of chains, updated references, and minor corrections

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• Knotted 3-balls in S^4
• On the automorphism groups of hyperbolic manifolds
• On automorphisms of high-dimensional solid tori
• The homology of moduli spaces of 4-manifolds may be infinitely generated