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.
Study Heegaard Floer homology of plumbed 3-manifolds, proving infinite-rank subgroup existence.
New infinite rank subgroups of knot concordance groups are constructed using algebraic solutions.
Satellite operators generate infinite rank subgroups in knot concordance.
We show that the subgroup of the knot concordance group generated by links of isolated complex singularities intersects the subgroup of algebraically slice knots in an infinite rank subgroup.
Study shows infinite-rank summand in homology cobordism group.
Satellite operations have infinite rank in smooth concordance group.
Study of Torelli group homology reveals infinite rank subgroups.
Infinite rank groups found in 3-manifolds with infinite fundamental groups.
New infinite-rank summand found in knot concordance group.
The paper constructs infinite rank summands in diffeomorphism groups via Seiberg-Witten theory.
We use moduli spaces of instantons and Chern-Simons invariants of flat connections to prove that the Whitehead doubles of (2,2^n-1) torus knots are independent in the smooth knot concordance group; that is, they freely generate a subgroup of infinite rank.
We provide new information about the structure of the abelian group of topological concordance classes of knots in . One consequence is that there is a subgroup of infinite rank consisting entirely of knots with vanishing Casson-Gordon invariants but whose non-triviality is detected by signatures.
Study satellite operations on Upsilon invariant of knots.
New knots not rationally concordant to their reverses found.
New subgroup found in knot homology concordance group.
We give an explicit construction of linearly independent families of knots arbitrarily deep in the (n)-solvable filtration of the knot concordance group using the ρ^1-invariant. A difference between previous constructions of infinite rank subgroups in the concordance group and ours is that the deepest infecting knots i…
In this note, we prove a lower bound for the positive kinkiness of a closed braid which we then use to derive an estimate for the positive kinkiness of a link in terms of its Seifert system. As an application, we show that certain pretzel knots cannot be unknotted using only positive crossing changes. We also describe …
New infinite-rank summand found in knot concordance group.
Infinite rank surface cluster algebras extend traditional concepts to surfaces with accumulation points.
Study shows complex K3 surfaces have infinite free abelian subgroup in their diffeomorphism group.
Study Brieskorn spheres using Floer homology, generating infinite rank summands in homology cobordism.
Study maps 4-manifolds with 1-handles, revealing infinite rank centers.
For a oriented genus g surface with one boundary component, S, the Torelli group is the group of orientation preserving homeomorphisms of S that induce the identity on homology. The Magnus representation of the Torelli group represents the action on F/F" where F=pi_1(S) and F" is the second term of the derived series. …
It is known that if any prime power branched cyclic cover of a knot in the 3-sphere is a homology sphere, then the knot has vanishing Casson-Gordon invariants. We construct infinitely many examples of (topologically) non-slice knots in the 3-sphere whose prime power branched cyclic covers are homology spheres. We show …
Consider the kernel Mag_g of the Magnus representation of the Torelli group and the kernel Bur_n of the Burau representation of the braid group. We prove that for g >= 2 and for n >= 6 the groups Mag_g and Bur_n have infinite rank first homology. As a consequence we conclude that neither group has any finite generating…
New findings on Johnson kernel's top homology group.
Study shows infinite-rank summand in homology concordance group of knots.
Free groups' automorphisms have bounded orbits.
New examples show satellite operations can expand the concordance group in topological knot theory.
We employ Hirzebruch-type invariants obtained from iterated p-covers to investigate concordance of links and string links. We show that the invariants naturally give various group homomorphisms of the string link concordance group into L-groups over number fields. We also obtain homomorphisms of successive quotients of…
The homology cobordism group of homology cylinders is a generalization of the mapping class group and the string link concordance group. We study this group and its filtrations by subgroups by developing new homomorphisms. First, we define extended Milnor invariants by combining the ideas of Milnor's link invariants an…
Study confirms conjectures for topologically slice knots' concordance group.
Study rational homology cobordisms of 3-spheres and lens spaces.
Study shows infinite rank in bipolar filtration of topologically slice knots.
Study satellite operators expanding concordance groups and their applications.
We construct equivariant, string and leading order characteristic classes and Chern-Simons classes for certain infinite rank bundles associated to fibrations occurring in loop spaces, Gromov-Witten theory and gauge theory. Results include a restatement of the S^1 index theorem using equivariant classes on the tangent b…
The paper shows infinite rank in T_1/T_2 and new insights into Alexander polynomials and concordance.
We describe an error in the proof of a key proposition, which was necessary for the proof of the main result. Alternate proofs of the main result are given by Ozsvath-Stipsicz-Szabo and Dai-Hom-Stoffregen-Truong.
The main goal of this article is to obtain a condition under which an infinite collection of satellite knots (with companion a positive torus knot and pattern similar to the Whitehead link) freely generates a subgroup of infinite rank in the smooth concordance group. This goal is attained by examining bot…
Obstructs 2-torsion in rational knot concordance group.
We define and study analogs of curve graphs for infinite type surfaces. Our definitions use the geometry of a fixed surface and vertices of our graphs are infinite multicurves which are bounded in both a geometric and a topological sense. We show that the graphs we construct are generally connected, infinite diameter a…
Chern-Weil and Chern-Simons theory extend to certain infinite-rank bundles that appear in mathematical physics. We discuss what is known of the invariant theory of the corresponding infinite-dimensional Lie groups. We use these techniques to detect cohomology classes for spaces of maps between manifolds and for diffeom…
For any group G, we define a new characteristic series related to the derived series, that we call the torsion-free derived series of G. Using this series and the Cheeger-Gromov rho-invariant, we obtain new real-valued homology cobordism invariants rho_n for closed (4k-1)-dimensional manifolds. For 3-dimensional manifo…
We consider the Grope filtration of the classical knot concordance group that was introduced in a paper of Cochran, Orr and Teichner. Our main result is that successive quotients at each stage in this filtration have infinite rank. We also establish the analogous result for the Grope filtration of the concordance group…
This paper presents a natural extension of stagewise ranking to the the case of infinitely many items. We introduce the infinite generalized Mallows model (IGM), describe its properties and give procedures to estimate it from data. For estimation of multimodal distributions we introduce the Exponential-Blurring-Mean-Sh…
Let T denote the group of smooth concordance classes of topologically sice knots. We show that the first quotient in the bipolar filtration of T (i.e. 0-bipolar knots modulo 1-bipolar knots) has infinite rank, even modulo Alexander polynomial one knots. Any 0-bipolar knot has vanishing tau-, epsilon-, and s-invariants.…
Constructs compactifications for median spaces with compact intervals.
We propose and analyze a structure with which to organize the difference between a knot in the 3-sphere bounding a topologically embedded 2-disk in the 4-ball and it bounding a smoothly embedded disk. The n-solvable filtration of the topological knot concordance group, due to Cochran-Orr-Teichner, may be complete in th…