Paper proves non-extendability of quasimorphism and non-vanishing of Reznikov's class.
problem Non-extendability of Shelukhin's quasimorphism and non-vanishing of Reznikov's class.
method Analyzing specific symplectic manifolds like blow-ups of tori and products of surfaces.
result Non-extendability of Shelukhin's quasimorphism and non-vanishing of Reznikov's class for certain symplectic manifolds.
The study examines spaces of non-extendable quasimorphisms for group pairs.
problem Analyzing the space of non-extendable quasimorphisms for group pairs.
method Established a five-term exact sequence of cohomology relative to bounded subcomplex.
result Proved stable commutator length equivalent to stable mixed commutator length for certain pairs.
Let G^ be a group and G its normal subgroup. In this paper, we study G^-invariant quasimorphisms on G which appear in symplectic geometry and low dimensional topology. As its application, we prove the non-existence of a section of the flux homomorphism on closed surfaces of higher genus. We also prove…
New result on symplectomorphisms on surfaces, showing vanishing cup product of fluxes.
problem Understanding commuting symplectomorphisms on surfaces.
method Refinement of non-extendability result for Py's Calabi quasimorphism.
result Vanishing cup product of fluxes for commuting symplectomorphisms.
Study symplectic and Hamiltonian actions on irrational ruled surfaces, proving existence and non-existence of extensions.
problem Tackles the extension of symplectic and Hamiltonian cyclic actions to Hamiltonian circle actions on irrational ruled symplectic 4-manifolds.
method Constructs symplectic involutions and cyclic actions, classifies symplectic morphisms, and proves non-extendability of certain actions.
result Shows existence and non-existence of Hamiltonian circle actions for different cyclic actions on irrational ruled symplectic 4-manifolds.
Survey on invariant quasimorphisms and their relation to stable commutator length.
problem Understanding the relationship between invariant quasimorphisms and stable commutator length.
method Review of existing methods and examples in invariant quasimorphisms and their relation to stable commutator length.
result The existence of non-extendable invariant quasimorphisms is closely related to the behavior of stable mixed commutator length.
Example of group action on surface that can't extend to 3-manifold.
problem Finding group actions on surfaces that can't be extended to 3-manifolds.
method Provided a first known example and sufficient conditions for infinitely many such actions.
result Finite group actions on surfaces that are free and orientation-preserving do not extend to arbitrary actions on 3-manifolds.
Building on the algebraic framework developed by Hendricks, Manolescu, and Zemke, we introduce and study a set of Floer-theoretic invariants aimed at detecting corks. Our invariants obstruct the extension of a given involution over any homology ball, rather than a particular contractible manifold. Unlike previous appro…
Unified proof of four Bavard dualities and new results on quasimorphisms.
problem Comparing stable commutator length and quasimorphisms on groups.
method Expository account and new strengthening of Bavard duality, providing complete proofs.
result Generalized mixed Bavard duality, recovering all previous dualities.
Researchers provide a simple topological method for Burau representations of loop braid groups.
problem Constructing Burau representations of loop braid groups.
method Simple topological construction of the Burau representations.
result One of the representations is more subtle and topologically natural but not easily combinatorially obvious.
New findings on plane waves in 3D spacetimes, showing non-unimodular elliptic plane waves are unique.
problem Classifying Lorentz homogeneous spaces of dimension 3, focusing on plane waves.
method Revisiting and relaxing usual completeness assumptions, characterizing homogeneous plane waves.
result Non-unimodular elliptic plane waves are unique and non-extendable, geodesically complete only if symmetric.
A complex structure on a subset of S^6 cannot be extended to a global integrable structure.
problem Non-integrability of complex structures on subsets of S^6.
method Proving the non-integrability of extensions of a specific complex structure on a subset of S^6.
result It is impossible to deform a non-integrable structure to an integrable one on S^6 while fixing it on a subset.
We revisit the problem of extension of a Killing vector field in a spacetime which is solution to the Einstein-Maxwell equation. This extension has been proved to be unique in the case of a Killing vector field which is normal to a bifurcate horizon by Yu. Here we generalize the extension of the vector field to a stron…
Extended signatures help distinguish non-concordant links.
problem Distinguishing non-concordant links using signatures.
method Defined and studied an n-variable extension of the Levine-Tristram signature, proving it a concordance invariant on a dense subset of the torus.
result Found an infinite family of 3-component links not concordant to their mirror images, detectable only by the extended signature.
New theory classifies knotted spheres in 4D space.
problem Classifying knotted punctured spheres in 4D space.
method Diagrammatic theory of welded graphs, Tube map extension, Milnor invariants.
result Complete link-homotopy classification of knotted punctured spheres.
Unified framework for solving linear systems with improved convergence rates.
problem Efficiently solving linear systems with randomized batch-sampling methods.
method Developed a unified randomized batch-sampling Kaczmarz framework with concentration inequalities for analysis.
result Derived new expected linear convergence rate bounds that are tighter and more reflective of empirical behavior.
By using a Borel density theorem for algebraic quotients, we prove a theorem concerning isometric actions of a Lie group G on a smooth or analytic manifold M with a rigid A-structure σ. It generalizes Gromov's centralizer and representation theorems to the case where R(G) is split solvable and $G/R(G…
Study on embeddings of surfaces in 4-manifolds and their mapping classes.
problem Characterizing and understanding embeddings of surfaces in 4-manifolds and their mapping classes.
method Analyzing smooth proper embeddings and mapping classes induced by diffeomorphisms of 4-manifolds.
result Most surfaces do not admit flexible embeddings in 4-manifolds with specific homology types.
This work interprets supergravity as a super Cartan geometry linking it to Yang-Mills theory.
problem Geometric interpretation of supergravity and its relation to Yang-Mills theory.
method Using enriched categories and super Cartan geometries, the authors link supergravity to Yang-Mills theory.
result Non-extended D=4 supergravity naturally arises in this framework.