ترغب بنشر مسار تعليمي؟ اضغط هنا

Higher order generalization of Fukayas Morse homotopy invariant of 3-manifolds I. Invariants of homology 3-spheres

247   0   0.0 ( 0 )
 نشر من قبل Tadayuki Watanabe
 تاريخ النشر 2012
  مجال البحث
والبحث باللغة English
 تأليف Tadayuki Watanabe




اسأل ChatGPT حول البحث

We give a generalization of Fukayas Morse homotopy theoretic approach for 2-loop Chern--Simons perturbation theory to 3-valent graphs with arbitrary number of loops at least 2. We construct a sequence of invariants of integral homology 3-spheres with values in a space of 3-valent graphs (Jacobi diagrams or Feynman diagrams) by counting graphs in an integral homology 3-sphere satisfying certain condition described by a set of ordinary differential equations.



قيم البحث

اقرأ أيضاً

81 - Tadayuki Watanabe 2016
In this paper, it is explained that a topological invariant for 3-manifold $M$ with $b_1(M)=1$ can be constructed by applying Fukayas Morse homotopy theoretic approach for Chern--Simons perturbation theory to a local system on $M$ of rational functio ns associated to the free abelian covering of $M$. Our invariant takes values in Garoufalidis--Rozanskys space of Jacobi diagrams whose edges are colored by rational functions. It is expected that our invariant gives a lot of nontrivial finite type invariants of 3-manifolds.
167 - Tadayuki Watanabe 2016
Garoufalidis and Levine defined a filtration for 3-manifolds equipped with some degree 1 map ($mathbb{Z}pi$-homology equivalence) to a fixed 3-manifold $N$ and showed that there is a natural surjection from a space of $pi=pi_1N$-decorated graphs to t he graded quotient of the filtration over $mathbb{Z}[frac{1}{2}]$. In this paper, we show that in the case of $N=T^3$ the surjection of Garoufalidis--Levine is actually an isomorphism over $mathbb{Q}$. For the proof, we construct a perturbative invariant by applying Fukayas Morse homotopy theoretic construction to a local system of the quotient field of $mathbb{Q}pi$. The first invariant is an extension of the Casson invariant to $mathbb{Z}pi$-homology equivalences to the 3-torus. The results of this paper suggest that there is a highly nontrivial equivariant quantum invariants for 3-manifolds with $b_1=3$. We also discuss some generalizations of the perturbative invariant for other target spaces $N$.
121 - Tatsuro Shimizu 2013
We define an invariant of rational homology 3-spheres via vector fields. The construction of our invariant is a generalization of both that of the Kontsevich-Kuperberg-Thurston invariant and that of Watanabes Morse homotopy invariant, which implies the equivalence of these two invariants.
94 - Delphine Moussard 2017
We study a theory of finite type invariants for null-homologous knots in rational homology 3-spheres with respect to null Lagrangian-preserving surgeries. It is an analogue in the setting of the rational homology of the Goussarov-Rozansky theory for knots in integral homology 3-spheres. We give a partial combinatorial description of the graded space associated with our theory and determine some cases when this description is complete. For null-homologous knots in rational homology 3-spheres with a trivial Alexander polynomial, we show that the Kricker lift of the Kontsevich integral and the Lescop equivariant invariant built from integrals in configuration spaces are universal finite type invariants for this theory; in particular it implies that they are equivalent for such knots.
242 - Tadayuki Watanabe 2015
We study finite type invariants of nullhomologous knots in a closed 3-manifold $M$ defined in terms of certain descending filtration ${mathscr{K}_n(M)}_{ngeq 0}$ of the vector space $mathscr{K}(M)$ spanned by isotopy classes of nullhomologous knots i n $M$. The filtration ${mathscr{K}_n(M)}_{n geq 0}$ is defined by surgeries on special kinds of claspers in $M$ having one special leaf. More precisely, when $M$ is fibered over $S^1$ and $H_1(M)=mathbb{Z}$, we study how far the natural surgery map from the space of $mathbb{Q}[t^{pm 1}]$-colored Jacobi diagrams on $S^1$ of degree $n$ to the graded quotient $mathscr{K}_n(M)/mathscr{K}_{n+1}(M)$ can be injective for $nleq 2$. 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 Lescops construction of $mathbb{Z}$-equivariant perturbative invariant of 3-manifolds.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا