Invariants of smooth 4-manifolds via Vassiliev theory

Details Invariants of smooth 4-manifolds via Vassiliev theory Invariants of smooth 4-manifolds via Vassiliev theory

2005-10-20

arxiv.org/abs/math/0510448v2

Mathematics

Geometric Topology

The above named paper has been withdrawn (see abstract for explanation)

Scientific paper

The above named paper has been withdrawn. A colleague has observed a gap in the proof of isotopy invariance, which can be repaired by reducing the coefficients (which lie in (1/6)Z) of the antisymmetric kanji with chords incident with more than one component modulo 8Z. An analogous issue arises in considering the effect of orientation reversal in the proof of handle-slide invariance, which can be repaired by reducing the coefficients of all of the antisymmetric kanji modulo 4Z. While an invariant of smooth 4-manifolds is obtained by the repaired construction, the corrected construction does not distinguish the smooth structures on the non-diffeomorphic but homeomorphic pairs of Gompf nuclei. A more subtle approach to restoring invariance, using an action of an extension of Gl(n,Z), rather than quotienting the coefficient, has been examined, but will also not restore the ability of the invariant constructed to distinguish the Gompf nuclei.

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