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Finite type invariants of nullhomologous...
Watanabe, Tadayuki...

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Finite type invariants of nullhomologous knots in 3-manifolds fibered over S1 by counting graphs by Watanabe, Tadayuki ( Author )
Lemonjar Open Access
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07-05-2015
We study finite type invariants of nullhomologous knots in a closed 3-manifold M defined in terms of certain descending filtration {Kn(M)}n≥0 of the vector space K(M) spanned by isotopy classes of nullhomologous knots in M. The filtration {Kn(M)}n≥0 is defined by surgeries on special kinds of claspers in M having one special leaf. More precisely, when M is fibered over S1 and H1(M)=Z, we study how far the natural surgery map from the space of Q[t±1]-colored Jacobi diagrams on S1 of degree n to the graded quotient Kn(M)/Kn+1(M) can be injective for n≤2. To do this, we construct a finite type invariant of nullhomologous knots in M up to degree 2 that is an analogue of the invariant given in our previous paper arXiv:1503.08735, which is based on Lescop's construction of Z-equivariant perturbative invariant of 3-manifolds.
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English
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MYR 0.00
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http://arxiv.org/abs/1505.01697
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