167 citations · 337 across the 25 of their papers we have counts for
27 papers
Index for a mutation loop
Tsukasa Ishibashi, Yuji Terashima
Motivated by the 3d-3d correspondence, we introduce an index for a mutation loop of a quiver and an integer . We prove its integrality $\mathcal{I}_…
Homological blocks with simple Lie algebras and Witten--Reshetikhin--Turaev invariants
Yuya Murakami, Yuji Terashima
In this article, for any Seifert fibered homology 3-sphere, we introduce homological blocks with simple Lie algebra and prove that its radial limits are identified with the Witten-…
Discrete Higher Berry Phases and Matrix Product States
Shuhei Ohyama, Yuji Terashima, Ken Shiozaki
A -parameter family of invertible states gives a topological transport phenomenon, similar to the Thouless pumping. As a natural generalization of this, we can consider a family…
Quantum invariants of closed framed -manifolds based on ideal triangulations
Serban Matei Mihalache, Sakie Suzuki, Yuji Terashima
We construct a new type of quantum invariant of closed framed -manifolds with the vanishing first Betti number. The invariant is defined for any finite dimensional Hopf algebra,…
On adjoint homological Selmer modules for SL-representations of knot groups
Takahiro Kitayama, Masanori Morishita, Ryoto Tange +1
We introduce the adjoint homological Selmer module for an SL-representation of a knot group, which may be seen as a knot theoretic analogue of the dual adjoint Selmer module fo…
Modular transformations of homological blocks for Seifert fibered homology -spheres
Toshiki Matsusaka, Yuji Terashima
In this article, for any Seifert fibered integral homology 3-sphere, we give explicit modular transformation formulas of homological blocks introduced by Gukov-Pei-Putrov-Vafa. Mor…
The colored Jones polynomials as vortex partition functions
Masahide Manabe, Seiji Terashima, Yuji Terashima
We construct 3D abelian gauge theories on labeled by knot diagrams whose K-theoretic vortex partition functions, each of which is…
The Heisenberg double of involutory Hopf algebras and invariants of closed -manifolds
Serban Matei Mihalache, Sakie Suzuki, Yuji Terashima
We construct an invariant of closed oriented -manifolds using a finite dimensional, involutory, unimodular and counimodular Hopf algebra . We use the framework of normal o-gr…
Arithmetic Orr invariants of absolute Galois groups
Hisatoshi Kodani, Yuji Terashima
Based on the analogies between mapping class groups and absolute Galois groups, we introduce an arithmetic pro- analogue of Orr invariants for a Galois element associated wit…
Witten-Reshetikhin-Turaev function for a knot in Seifert manifolds
Hiroyuki Fuji, Kohei Iwaki, Hitoshi Murakami +1
In this paper, for a Seifert loop (i.e., a knot in a Seifert three-manifold), first we give a family of an explicit function whose special values at roots of unity are id…
On -dimensional foliated dynamical systems and Hilbert type reciprocity law
Junhyeong Kim, Masanori Morishita, Takeo Noda +1
We show some fundamental results concerning -dimensional foliated dynamical systems (FDS for short) introduced by Deninger. Firstly, we give a decomposition theorem for an F…
Cluster variables, ancestral triangles and Alexander polynomials
Wataru Nagai, Yuji Terashima
In this paper, we show that Alexander polynomials for any 2-bridge knots are specializations of cluster variables. A key tool is an ancestral triangle which appeared in both quantu…
Quiver mutation sequences and -binomial identities
Akishi Kato, Yuma Mizuno, Yuji Terashima
In this paper, first we introduce a quantity called a partition function for a quiver mutation sequence. The partition function is a generating function whose weight is a -binom…
Arithmetic topology in Ihara theory
Hisatoshi Kodani, Masanori Morishita, Yuji Terashima
Ihara initiated to study a certain Galois representation which may be seen as an arithmetic analogue of the Artin representation of a pure braid group. We pursue the analogies in I…
Homotopy theory of -algebras and characteristic classes of fiber bundles
Hiroshige Kajiura, Takahiro Matsuyuki, Yuji Terashima
In this paper we give a Chern-Weil-type construction of characteristic classes of fiber bundles, based on homotopy theory of C-infinity algebras. Our idea is to replace a family of…
Characteristic classes of fiber bundles
Takahiro Matsuyuki, Yuji Terashima
In this paper, we construct new characteristic classes of fiber bundles via flat connections with values in infinite-dimensional Lie algberas of derivations. In fact, choosing a fi…
On certain L-functions for deformations of knot group representations
Takahiro Kitayama, Masanori Morishita, Ryoto Tange +1
We study the twisted knot module for the universal deformation of an -representation of a knot group, and introduce an associated -function, which may be seen as an…
On the universal deformations for SL_2-representations of knot groups
Masanori Morishita, Yu Takakura, Yuji Terashima +1
Based on the analogies between knot theory and number theory, we study a deformation theory for SL_2-representations of knot groups, following after Mazur's deformation theory of G…
Quantum dilogarithms and partition q-series
Akishi Kato, Yuji Terashima
In our previous work [arXiv:1403.6569], we introduced the partition q-series for mutation loop --- a loop in exchange quiver. In this paper, we show that for certain class of mutat…
Quiver mutation loops and partition q-series
Akishi Kato, Yuji Terashima
A quiver mutation loop is a sequence of mutations and vertex relabelings, along which a quiver transforms back to the original form. For a given mutation loop, we introduce a quant…
-Johnson homomorphisms and pro-p groups
Masanori Morishita, Yuji Terashima
We propose an approach to study non-Abelian Iwasawa theory, using the idea of Johnson homomorphisms in low dimensional topology. We introduce arithmetic analogues of Johnson homomo…
Torsion functions on moduli spaces in view of the cluster algebra
Takahiro Kitayama, Yuji Terashima
We introduce non-acyclic -torsion of a 3-manifold with toroidal boundary as an extension of J. Porti's -torsion, and present an explicit formu…
3d N=2 Theories from Cluster Algebras
Yuji Terashima, Masahito Yamazaki
We propose a new description of 3d theories which do not admit conventional Lagrangians. Given a quiver and a mutation sequence on it, we define a 3d $\math…
Emergent 3-manifolds from 4d Superconformal Indices
Yuji Terashima, Masahito Yamazaki
We show that the smooth geometry of a hyperbolic 3-manifold emerges from a classical spin system defined on a 2d discrete lattice, and moreover show that the process of this "dimen…