Constructs closed aspherical 4-manifolds that are homeomorphic but not diffeomorphic, providing counterexamples to the smooth Borel conjecture in dimension 4.
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Knot traces of alternating knots and the newly defined extended alternating knots admit PALFs whose regular fibers have genus equal to the number of white regions in their planar graphs.
A combinatorial extension of a PALF construction produces genus-1 fiber versions on knot traces of Legendrian positive twist knots and positive torus knots T_{2,2n+1} while preserving the diffeomorphism type of the total space.
citing papers explorer
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Exotic aspherical 4-manifolds
Constructs closed aspherical 4-manifolds that are homeomorphic but not diffeomorphic, providing counterexamples to the smooth Borel conjecture in dimension 4.
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Lefschetz Fibrations on Knot Traces of Alternating and Extended Alternating Knots
Knot traces of alternating knots and the newly defined extended alternating knots admit PALFs whose regular fibers have genus equal to the number of white regions in their planar graphs.
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Combinatorial extension of a simple construction of Lefschetz fibrations
A combinatorial extension of a PALF construction produces genus-1 fiber versions on knot traces of Legendrian positive twist knots and positive torus knots T_{2,2n+1} while preserving the diffeomorphism type of the total space.