اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn certain L-functions for deformations of knot group representations
307
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We study the twisted knot module for the universal deformation of an ${rm SL}_2$-representation of a knot group, and introduce an associated $L$-function, which may be seen as an analogue of the algebraic $p$-adic $L$-function associated to the Selmer module for the universal deformation of a Galois representation. We then investigate two problems proposed by Mazur: Firstly we show the torsion property of the twisted knot module over the universal deformation ring under certain conditions. Secondly we verify the simplicity of the zeroes of the $L$-function by some concrete examples for 2-bridge knots.
قيم البحث
اقرأ أيضاً
Given a homomorphism from a link group to a group, we introduce a $K_1$-class in another way, which is a generalization of the 1-variable Alexander polynomial. We compare the $K_1$-class with $K_1$-classes in cite{Nos} and with Reidemeister torsions.
As a corollary, we show a relation to Reidemeister torsions of finite cyclic covering spaces, and show reciprocity in some senses.
We show that one of the Cappell-Shaneson knot complements admits an extraordinarily small triangulation, containing only two 4-dimensional simplices.
Given a grid diagram for a knot or link K in $S^3$, we construct a spectrum whose homology is the knot Floer homology of K. We conjecture that the homotopy type of the spectrum is an invariant of K. Our construction does not use holomorphic geometry,
but rather builds on the combinatorial definition of grid homology. We inductively define models for the moduli spaces of pseudo-holomorphic strips and disk bubbles, and patch them together into a framed flow category. The inductive step relies on the vanishing of an obstruction class that takes values in a complex of positive domains with partitions.
This paper studies the moduli space of solutions to the Bogomolny equation on R^3 with a certain type of knot singularity. For technical reasons, I have to assume the monodromy along the meridian of the knot lies in (0, 1/8) or in (3/8, 1/2) and I do
nt know how to resolve this constraint. The main result of this paper is: a neighbourhood of a solution to the Bogomolny equations on R^3 with such knot singularity in the moduli space has an analytical structure. Moreover, certain solutions (that come from gluing a model solution with the knot singularity and classical regular solutions) have a neighbourhood in the moduli space that has a manifold structure.
We develop a theory of equivariant group presentations and relate them to the second homology group of a group. Our main application says that the second homology group of the Torelli subgroup of the mapping class group is finitely generated as an $Sp(2g,mathbb{Z})$-module.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
