A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
A new knot move preserves pass-move equivalence and differs in count.
It is well known that any two diagrams representing the same oriented link are related by a finite sequence of Reidemeister moves O1, O2 and O3. Depending on orientations of fragments involved in the moves, one may distinguish 4 different versions of each of the O1 and O2 moves, and 8 versions of the O3 move. We introd…
In this paper, we introduce an equivalence relation on the set of local moves and classify local moves, called the extended -moves, up to the equivalence. Moreover, by inducing a binary relation on the set of equivalence classes of local moves, we show that an extended -move realizes the crossing change or the …
Minimal sets of moves for isotopic knots and trivalent graphs identified.
The H(n)-move simplifies virtual and welded knots and links.
We prove that the classical set of moves for standard spines of 3-manifolds (i.e. the MP-move and the V-move) does not suffice to relate to each other any two standard skeleta of a 3-manifold with marked boundary. We also describe a condition on the 3-manifold with marked boundary that tells whether the generalised set…
The (ordinary) unknotting-number of 1-dimensional knots, which is defined by using the crossing-change, is a very basic and important invariant. It is very natural to consider the `unknotting-number' associated with other local-moves on n-dimensional knots, where n is a natural number. In this paper we prove the follow…
New rational band moves simplify knot classification.
We prove that the crossing changes, Delta moves, and sharp moves are unknotting operations on welded knots.
New methods for delta-moves on algebraically split links identified.
Minimal moves for surfaces in 4D discovered, linking planar and spatial moves.
Study virtualized Delta, Sharp, and Pass moves for oriented virtual knots and links.
Minimal generating sets of Reidemeister moves identified and classified.
We start a systematic analysis of links up to 5-move equivalence. Our motivation is to develop tools which later can be used to study skein modules based on the skein relation being deformation of a 5-move (in an analogous way as the Kauffman skein module is a deformation of a 2-move, i.e. a crossing change). Our main …
New diagonal move simplifies knots and links efficiently.
New moves help untangle complex knots.
Minimal moves for surfaces in 4D identified.
New virtualized Δ-move simplifies virtual knots and links.
Algorithm for recognizing and performing Reidemeister moves in Gauss diagrams.
Minimal sets of moves for rotational Reidemeister diagrams are identified.
The -move is a local move generated by forbidden moves in virtual knot theory. This move was introduced by Taniguchi and the second author, who showed that it characterizes the odd writhe of virtual knots, which is a fundamental invariant defined by Kauffman. In this paper, we extend this result by classifying -c…
4-move kills Alexander polynomial
Complete classification of links up to specific moves.
We show Vector Autoregressive Moving Average models with scalar Moving Average components could be estimated by generalized least square (GLS) for each fixed moving average polynomial. The conditional variance of the GLS model is the concentrated covariant matrix of the moving average process. Under GLS the likelihood …
Roseman moves are seven types of local modification for surface-link diagrams in -space which generate ambient isotopies of surface-links in -space. In this paper, we focus on Roseman moves involving triple points, one of which is the famous tetrahedral move, and discuss their independence. For each diagram of an…
In this paper, we formulate a new local move on virtual knot diagram, called arc shift move. Further, we extend it to another local move called region arc shift defined on a region of a virtual knot diagram. We establish that these arc shift and region arc shift moves are unknotting operations by showing that any virtu…
We describe various handle moves in contact surgery diagrams, notably contact analogues of the Kirby moves. As an application of these handle moves, we discuss the respective classifications of long and loose Legendrian knots.
In the present paper, we consider local moves on classical and welded diagrams: (self-)crossing change, (self-)virtualization, virtual conjugation, Delta, fused, band-pass and welded band-pass moves. Interrelationship between these moves is discussed and, for each of these move, we provide an algebraic classification. …
New moves prove crossing number sum for knots.
Analyses cohomology relations for moving frames and coframes.
A marked graph diagram is a link diagram possibly with marked -valent vertices. S. J. Lomonaco, Jr. and K. Yoshikawa introduced a method of representing surface-links by marked graph diagrams. Specially, K. Yoshikawa gave local moves on marked graph diagrams, nowadays called Yoshikawa moves. It is now known that two…
The forbidden moves can be combined with Gauss diagram Reidemeister moves to obtain move sequences with which we may change any Gauss diagram (and hence any virtual knot) into any other, including in particular the unknotted diagram
New moves for singular knots identified and described.
A C_n-move is a local move on links defined by Habiro and Goussarov, which can be regarded as a `higher order crossing change'. We use Milnor invariants with repeating indices to provide several classification results for links up to C_n-moves, under certain restrictions. Namely, we give a classification up to C_4-move…
New contact Kirby moves complete the set for contact surgery diagrams.
New sequences prove some link diagrams can't be transformed by specific moves.
New moving average adapts weight dynamically based on polynomial and wavefunction.
The paper extends CF-moves to classify virtual links of any number of components.
This study simplifies verification of invariants in oriented virtual knots.
Study on unknotting twisted knots using arc shift and region arc shift moves.
In a previous paper, the authors proved that Milnor link-homotopy invariants modulo classify classical string links up to -move and link-homotopy. As analogues to the welded case, in terms of Milnor invariants, we give here two classifications of welded string links up to -move and self-crossing virtualizat…
Discussing moving frames for curve and surface invariants.
Essential triangulations of certain manifolds are connected via specific moves.
Simplified combinatorial descriptions of branched spines for 3-manifolds using primary MP move and sliding moves.
Moving between 3-manifold triangulations is NP-hard
The L-move for classical braids extends naturally to trivalent braids. We follow the L-move approach to the Markov Theorem, to prove a one-move Markov-type theorem for trivalent braids. We also reformulate this L-Move Markov theorem and prove a more algebraic Markov-type theorem for trivalent braids. Along the way, we …
A pants-block decomposition of a 3-manifold is similar to a triangulation of a 3-manifold in many aspects. In this paper we show that any two pants-block decompositions of a 3-manifold are related by a finite sequence of moves which are called P-moves. The P-moves between pants-block decompositions are similar to the P…
A C_k-move is a local move that involves (k+1) strands of a link. A C_k-move is called a C_k^d-move if these (k+1) strands belong to mutually distinct components of a link. Since a C_k^d-move preserves all k-component sublinks of a link, we consider the converse implication: are two links with common k-component sublin…