New spines found in complex 4D shapes.
problem Finding spines in complex 4D shapes.
method Examined Levine and Lidman's constructions and found new spines.
result Infinitely many 4-manifolds have topological spines.
On-device research index
arXiv research
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.
168,982 papers · 148 categories
Trend · papers per month
27 results for “Lidman”
A 2018 paper proves a unique 4-manifold with a boundary homotopy equivalent to a sphere but no simplicial embedding.
problem Existence of a specific type of embedding in a 4-manifold.
method Proof of existence of a 4-manifold with boundary homotopy equivalent to a sphere but no simplicial embedding.
result A compact smooth 4-manifold with boundary homotopy equivalent to a sphere but no simplicial embedding.
We show that any exceptional non-trivial Dehn surgery on a twist knot, except the trefoil, yields a 3-manifold whose fundamental group is left-orderable. This is a generalization of a result of Clay, Lidman and Watson, and also gives a new supporting evidence for a conjecture of Boyer, Gordon and Watson.
New knot invariants from covering involutions help deduce linear independence results.
problem Understanding the smooth concordance group of knots.
method Covering involutions and adapted ideas from previous research.
result Novel linear independence results in the smooth concordance group of knots.
GRID invariants block certain Lagrangian cobordisms in 3D.
problem Obstructing decomposable Lagrangian cobordisms in 3D.
method Filtered GRID invariants and link Floer homology.
result GRID invariants obstruct decomposable Lagrangian cobordisms.
New exotic structures found on 4-manifolds with specific groups.
problem Finding exotic smooth structures on 4-manifolds with certain fundamental groups.
method Constructing new smooth structures using definite intersection forms and fundamental groups.
result Infinitely many exotic smooth structures on 4-manifolds with fundamental group Z/2Z.
Ribbon cobordisms form a partial order on 3-manifolds.
problem Understanding the partial order structure of 3-manifolds.
method Building on Agol's proof for knots, we extend the partial order to 3-manifolds.
result Ribbon rational homology cobordism forms a partial order.
Study ribbon homology concordances using link Floer homology.
problem Understanding ribbon homology concordances and their effects on link Floer homology.
method Combining results from Daemi, Lidman, Vela-Vick, Wong, and Zemke, using link Floer homology and torsion submodules.
result Ribbon homology concordances induce split injections on .
Study monopole h-invariants from a topological viewpoint.
problem Understanding the h-invariants of 3-manifolds.
method Using Lidman and Manolescu's description of monopole Floer homology.
result Prove several properties of the h-invariants.
Proves special alternating knots can't have cosmetic crossings.
problem Cosmetic crossing changes in special alternating knots.
method Combines Lidman-Moore and Scharlemann-Thompson results.
result Special alternating knots do not admit non-nugatory crossing changes.
Study shows knots with specific properties avoid certain topological surgeries.
problem Understanding knots and their behavior under specific surgeries.
method Analyzes null-homotopic knots in 3-manifolds and their effect on surgeries.
result Zero surgery on null-homotopic knots in certain 3-manifolds avoids summands of .
Using Hirasawa-Murasugi's classification of fibered Montesinos knots we classify the L-space Montesinos knots, providing further evidence towards a conjecture of Lidman-Moore that L-space knots have no essential Conway spheres. In the process, we classify the fibered Montesinos knots whose open books support the tight …
We compute the connected Heegaard Floer homology (defined by Hendricks, Hom, and Lidman) for a large class of 3-manifolds, including all linear combinations of Seifert fibered homology spheres. We show that for such manifolds, the connected Floer homology completely determines the local equivalence class of the associa…
We give a method for constructing a Legendrian representative of a knot in which realizes its maximal Thurston-Bennequin number under a certain condition. The method utilizes Stein handle decompositions of , and the resulting Legendrian representative is often very complicated (relative to the complexity of …
Surgery obstructions extended to integer homology spheres using Heegaard Floer homology.
problem Obstructing knots in integer homology spheres using surgery.
method Extending Heegaard Floer homology obstructions to all integer homology spheres for both positive and negative surgeries.
result Deduced a lower bound on for smooth cobordism between integer homology spheres.
Study shows alternating knots can't have similar crossings.
problem Cosmetic crossings in alternating knots.
method Examined homology groups of 4-manifolds.
result Subgroups of knot homology groups have co-prime orders.
Alexander polynomial condition blocks crossing changes in some knots.
problem Cosmetic crossing changes in knot diagrams.
method Alexander polynomial obstruction for -space knots.
result Proved the conjecture for a five-parameter family of pretzel knots.
New proof shows certain 3D shapes can't be instanton L-spaces.
problem Proving certain 3D shapes cannot be instanton L-spaces.
method Proving by gluing complements of knots and analyzing their fundamental groups.
result Proven that the resulting 3-manifold cannot be an instanton L-space.
Kirby diagrams for exotic R^4's constructed from specific knot complements.
problem Identifying and visualizing exotic 's using Kirby diagrams.
method Provided Kirby diagrams for a family of exotic 's constructed from specific knot complements.
result Generalized Kirby diagrams for a broader family of exotic 's.
New applications of trace embedding lemma show exotic 4-manifolds properties.
problem Detecting exotic phenomena in 4-dimensional smooth structures.
method New applications of trace embedding lemma to study piecewise-linear surfaces.
result Found infinitely many pairs of homeomorphic 4-manifolds with distinct properties.
Study shows knots in homology spheres can be topologically equivalent to those in .
problem Distinguishing knots in homology spheres from those in .
method Whitney tower filtration of concordance and solvable filtration.
result Every knot (or link) in a homology sphere is equivalent to a knot (or link) in modulo any term in the Whitney tower filtration.
New invariant recovers known contact element and considers finite coverings.
problem Defining and studying new contact invariants in Seiberg-Witten Floer spectra.
method Cohomotopy set of Seiberg-Witten Floer spectrum, equivariant Borel cohomology.
result New invariant recovers known contact element and considers finite coverings.
The paper explores surgeries on lens spaces and their knot properties.
problem Characterizing surgeries on lens spaces that yield specific lens spaces.
method Distance one surgeries and Heegaard Floer mapping cone formula.
result Conditions for obtaining lens spaces via distance one surgeries.
This paper gives a geometric interpretation of bordered Heegaard Floer homology for manifolds with torus boundary. If is such a manifold, we show that the type D structure may be viewed as a set of immersed curves decorated with local systems in . These curves-with-decoration ar…
Computes monopole Floer homology for three-manifolds.
problem Computing monopole Floer homology for three-manifolds.
method Develops a new framework to study homotopical properties of dga twisted with a specific kind of Maurer-Cartan element, and computes higher operations for the torus.
result Explicit computation of for the torus.
Detect slopes in toroidal 3-manifolds to prove properties of fundamental groups.
problem Prove properties of fundamental groups of toroidal 3-manifolds.
method Slope detection using left-orders, foliations, and Heegaard Floer homology.
result Toroidal integer homology spheres have left-orderable fundamental groups.
Formula calculates instanton homology dimensions for knot surgeries over arbitrary fields.
problem Calculating instanton homology dimensions for knot surgeries over arbitrary fields.
method Established a dimension formula for framed instanton homology of knot surgeries over arbitrary fields.
result Formula generalizes instanton homology dimensions to arbitrary fields, including new results for and knots.