On definite lattices bounded by a homology 3–sphere and Yang–Mills instanton Floer theory

Scaduto, Christopher¹

¹ Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, NY, United States, Department of Mathematics, University of Miami, Coral Gables, FL, United States

Geometry & topology, Tome 28 (2024) no. 4, pp. 1587-1628.

Résumé

Using instanton Floer theory, extending methods due to Frøyshov, we determine the definite lattices that arise from smooth $4$–manifolds bounded by certain homology $3$–spheres. For example, we show that for $+1$ surgery on the (2,5) torus knot, the only nondiagonal lattices that can occur are $E_8$ and the indecomposable unimodular definite lattice of rank 12, up to diagonal summands. We require that our $4$–manifolds have no $2$–torsion in their homology.

Détail

DOI : 10.2140/gt.2024.28.1587

Classification : 57R57, 57M99
Keywords: instanton, Floer homology, 4–manifolds

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