A link surgery spectral sequence in monopole Floer homology - Mathematics > Geometric TopologyReport as inadecuate




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Abstract: To a link L in the 3-sphere, we associate a spectral sequence whose E^2 pageis the reduced Khovanov homology of L and which converges to a version of themonopole Floer homology of the branched double cover. The pages E^k for k > 1depend only on the mutation equivalence class of L. We define a mod 2 gradingon the spectral sequence which interpolates between the delta-grading onKhovanov homology and the mod 2 grading on Floer homology. We also derive a newformula for link signature that is well-adapted to Khovanov homology.More generally, we construct new bigraded invariants of a framed link in a3-manifold as the pages of a spectral sequence modeled on the surgery exacttriangle. The differentials count monopoles over families of metricsparameterized by permutohedra. We utilize a connection between the topology oflink surgeries and the combinatorics of graph associahedra. This also yieldssimple realizations of permutohedra and associahedra, as refinements ofhypercubes.



Author: Jonathan M. Bloom

Source: https://arxiv.org/







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