New homology spheres found with special knots.
problem Finding homology spheres with specific knots.
method Infinitely many homology spheres constructed.
result Two distinct knots with special surgeries found.
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We construct link invariants using the subfactor planar algebras, and use these to prove new identities relating certain specializations of colored Jones polynomials to specializations of other quantum knot polynomials. These identities can also be explained by coincidences between small modular categories inv…
Geometrically computes cohomotopy groups for higher-dimensional manifolds.
problem Computing cohomotopy groups for higher-dimensional manifolds.
method Geometric arguments and introduction of new manifold types.
result Refined Euler class and obstruction to non-vanishing sections.