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3 results for “Y-filtration”

Abelian quotients of the

Y

-filtration on the homology cylinders via the LMO functormath.GT

New homomorphisms from homology cylinders to torsion modules via LMO functor.

problem Understanding the abelian quotients of homology cylinders.

method Constructing homomorphisms via LMO functor and analyzing their properties.

result Abelianization of Johnson kernel has torsion elements.

homology cylinders LMO functor Johnson homomorphism torsion elements Y-filtration

2020-01-27abs ↗pdf ↗

Torsion elements in the associated graded of the

Y

-filtration of the monoid of homology cylindersmath.GT

This paper detects torsion elements in homology cylinder monoids.

problem Detecting torsion elements in the associated graded of the Y-filtration of homology cylinders.

method Introduced a homomorphism induced by the LMO functor to detect torsion elements.

result Every non-trivial torsion element in

Y_6\mathcal{IC}/Y_7

has order 3.

torsion elements homology cylinders Y-filtration LMO functor claspers

2024-10-14abs ↗pdf ↗

Symplectic Jacobi diagrams and the Lie algebra of homology cylindersmath.GT

Let S be a compact connected oriented surface, whose boundary is connected or empty. A homology cylinder over the surface S is a cobordism between S and itself, homologically equivalent to the cylinder over S. The Y-filtration on the monoid of homology cylinders over S is defined by clasper surgery. Using a functorial …

2007-12-01abs ↗pdf ↗