An invariant of link cobordisms from symplectic Khovanov homology - Mathematics > Symplectic GeometryReportar como inadecuado




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Abstract: Symplectic Khovanov homology is an invariant of oriented links defined bySeidel and Smith and conjectured to be isomorphic to Khovanov homology. Idefine morphisms up to a global sign ambiguity between symplectic Khovanovhomology groups, corresponding to isotopy classes of smooth link cobordisms in4D between a fixed pair of links. These morphisms define a functor from thecategory of links and such cobordisms to the category of abelian groups andgroup homomorphisms up to a sign ambiguity. This provides an extra structurefor symplectic Khovanov homology and more generally an isotopy invariant ofsmooth surfaces in 4D; a first step in proving the conjectured isomorphism ofsymplectic Khovanov homology and Khovanov homology. The maps themselves aredefined using a generalisation of Seidel-s relative invariant of exactLefschetz fibrations to exact Morse-Bott-Lefschetz fibrations with non-compactsingular loci.



Autor: Jack W. Waldron

Fuente: https://arxiv.org/







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