The purpose of this paper is to construct and study equivariant Khovanov homology - a version of Khovanov homology theory for periodic links. Since our construction works regardless of the characteristic of the coefficient ring it generalizes a previous construction by Chbili. We establish invariance under equivariant …
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Equivariant primitive harmonic maps into symmetric spaces, with applications to Willmore surfacesmath.DG
The study constructs equivariant harmonic maps into symmetric spaces with applications to Willmore surfaces.
problem Constructing harmonic maps into symmetric spaces.
method Equivariant primitive harmonic maps construction.
result Examples of -equivariant Willmore Moebius strips in .
We study the existence of -equivariant characteristic classes on certain natural infinite rank bundles over the loop space of a manifold . We discuss the different -equivariant cohomology theories in the literature and clarify their relationships. We attempt to use -equivariant Chern-Weil techniq…
We introduce an equivariant Pontrjagin-Thom construction which identifies equivariant cohomotopy classes with certain fixed point bordism classes. This provides a concrete geometric model for equivariant cohomotopy which works for any compact Lie group G. In the special case when G is finite or a torus, we show that ou…
A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscs.LG
New method constructs equivariant neural networks for arbitrary matrix groups.
problem Challenges in constructing equivariant neural networks for complex groups.
method Completely general algorithm for solving equivariant layers of matrix groups.
result Constructs multilayer perceptrons equivariant to multiple groups including O(1,3), O(5), Sp(n), and Rubik's cube group.
Two constructions of Chern character for equivariant vector bundles in noncommutative geometry.
problem Chern character for equivariant vector bundles in noncommutative geometry.
method Two constructions using cyclic cohomology of crossed product algebras.
result Equivalence of two constructions under proper action.
Constructs singular Yamabe solutions via equivariant reduction.
problem Constructs non-trivial geometric examples for the Yamabe equation.
method Reduces the problem to an equivariant setting for simpler analysis.
result Provides a non-trivial weak solution to the Yamabe problem.
Constructs a functor for equivariant smooth h-cobordisms.
problem Defines a functor for equivariant smooth h-cobordisms.
method Constructs an -functor mapping smooth -manifolds to spaces of equivariant h-cobordisms.
result The functor structure is subtle and relies on new ideas.
Group-equivariant subsampling layers improve CNNs' equivariance.
problem Non-translation equivariance in subsampling operations.
method Translation and group-equivariant subsampling/upsampling layers.
result Group-equivariant autoencoders learn equivariant representations.
Constructs harmonic maps between special geometric shapes.
problem Creating harmonic maps between specific types of geometric shapes.
method Equivariant harmonic maps constructed between cohomogeneity one manifolds.
result Developed a method to construct harmonic maps.
Constructs equivariant embeddings of Hermitian symmetric spaces into tangent spaces.
problem Embedding Hermitian symmetric spaces into their tangent spaces.
method Using polarity of the K-action to construct equivariant embeddings.
result Characterizes holomorphic/symplectic embeddings and realizes submanifolds.
New method for Lagrangian Floer homology groups using flow trees.
problem Computing equivariant Lagrangian Floer homology.
method Constructing and exploiting an A-infinity module structure on the Floer complex.
result Established constructions of equivariant Lagrangian Floer homology groups.
We construct for an equivariant cohomology theory for proper equivariant CW-complexes an equivariant Chern character, provided that certain conditions about the coefficients are satisfied. These conditions are fulfilled if the coefficients of the equivariant cohomology theory possess a Mackey structure. Such a structur…
Unified theorem for deep and shallow joint-equivariant machines.
problem Universal approximation of joint-equivariant machines.
method Constructive universal approximation theorem based on ridgelet transform.
result Unified approximation of deep and shallow networks.
Let G be a compact Lie group. Let M be a smooth G-manifold and V --> M be an oriented G-equivariant vector bundle. One defines the spaces of equivariant forms with generalized coefficients on V and M. An equivariant Thom form on V is a compactly supported closed equivariant form such that its integral along the fib…
Paper develops equivariant basic cohomology for Lie groupoids.
problem Equivariant cohomology for Lie groupoids with weak actions.
method Using Kan fibrations and fiber structures, constructing models and comparing with existing theories.
result Equivariant basic cohomology theory for orbifolds and Lie groupoids.
New equivariant version of Khovanov homology for annuli.
problem Developing a new mathematical framework for annular Khovanov homology.
method Using Frobenius algebra and equivariant cohomology of .
result Introduced an equivariant version of the Temperley-Lieb algebra.
Study on equivariant Q-sliceness for strongly invertible knots.
problem Understanding Q-sliceness for strongly invertible knots.
method Constructive and obstructive approaches using Fox-Milnor condition and equivariant concordance.
result Klein amphichiral knots are equivariant Q-slice in a single Q-homology 4-ball.
Study calculates Floer homology for binary polyhedral spaces.
problem Calculating Floer homology for specific polyhedral spaces.
method Equivariant instanton Floer homology, modified algebraic construction.
result Equivariant instanton Floer homology values for binary polyhedral spaces.
Develops equivariant Seiberg-Witten-Floer cohomology for 3-spheres.
problem Finite group actions on rational homology 3-spheres.
method Equivariant version of Seiberg-Witten-Floer stable homotopy type.
result Definition of -invariants with Froyshov-type inequality.
Constructs equivariant analytic torsion for proper actions on manifolds.
problem Analytic torsion for proper actions on Riemannian manifolds.
method Equivariant construction of Ray-Singer analytic torsion for proper, isometric actions.
result Generalizes earlier results to noncompact conjugacy classes under suitable conditions.
Let be a compact, simply connected simple Lie group. We give a construction of an equivariant gerbe with connection on , with equivariant 3-curvature representing a generator of . Technical tools developed in this context include a gluing construction for gerbes and a theory of equivariant bundle ge…
New sl(2) action defined on a mathematical module.
problem No specific problem stated; focuses on mathematical construction.
method Construction of sl(2)-action on equivariant skein lasagna module.
result Infinitesimal sl(2)-symmetries constructed.
A refined form of the `Folk Theorem' that a smooth action by a compact Lie group can be (canonically) resolved, by iterated blow up, to have unique isotropy type was established by the authors in the context of manifolds with corners; the canonical construction induces fibrations on the boundary faces of the resolution…
We use contact geometry to describe the monoid of projectively equivariant meromorphic differential operators on a complex curve, quantization of which generalizes known constructions of classical equivariants to non-commutative function algebras in several variables.
Study stabilizes Morse-Bott cohomology for equivariant manifolds.
problem Equivariant cohomology of manifolds with group actions.
method Stabilization technique to construct Morse-Bott functions.
result Realization of equivariant transversality and orientability.
For a rational homology 3-sphere with a $\spinc$ structure $\s$, we show that simple algebraic manipulations of our construction of equivariant Seiberg-Witten Floer homology lead to a collection of variants which are topological invariants. We establish exact sequences relating them, we show that they satisfy a dua…
Equivalent bicategories constructed from action Lie groupoids.
problem Equivalence of bicategories constructed from action Lie groupoids.
method Localizing at equivariant weak equivalences, surjective submersive equivariant weak equivalences, and all weak equivalences.
result Weak equivalences between action Lie groupoids are isomorphic to compositions of nice forms of equivariant weak equivalences.
Study equivariant 4-genus of knots in symmetric 4-manifolds.
problem Understanding equivariant 4-genus of knots in symmetric 4-manifolds.
method Developed techniques for constructing slice disks via equivariant tubing construction.
result Equivariant 4-genus can differ from standard and equivariant 4-genus of 4-manifolds.
Generalizes Floer homotopy via Morse-Bott theory.
problem Constructing equivariant models in Floer theory.
method Morse-Bott theory, flow categories, stable homotopy types.
result Equivalence of Borel equivariant spectra for certain Lagrangians.
The paper constructs bundles and recovers Kirillov character formula.
problem Constructing smooth vector bundles over deformation to the normal cone.
method Rescaling of vector bundles and equivariant constructions.
result Recovery of Kirillov character formula for equivariant index.
Classifies 3-manifold groups with equivariant hierarchically hyperbolic structures.
problem Classifying 3-manifold groups with equivariant hierarchically hyperbolic structures.
method Construction of suitable quasimorphisms on Seifert pieces to construct actions on quasi-lines.
result 3-manifold groups admit equivariant hierarchically hyperbolic structures.
Study symmetries in equivariant Khovanov homology.
problem Understand symmetries in equivariant Khovanov homology.
method Construction of an involution, integral lifting, splitting of theories, and relation to Rasmussen's invariant.
result Established symmetries in equivariant Khovanov homology.
Characterizes a specific type of neural network for alternating group equivariance.
problem Understanding and characterizing neural networks with alternating group equivariance.
method Characterization of all possible -equivariant neural networks using tensor powers of .
result Found a basis of matrices for learnable, linear -equivariant layer functions.
We construct a new equivariant cohomology theory for a certain class of differential vertex algebras, which we call the chiral equivariant cohomology. A principal example of a differential vertex algebra in this class is the chiral de Rham complex of Malikov-Schechtman-Vaintrob of a manifold with a group action. The ma…
We define four versions of equivariant instanton Floer homology ( and ) for a class of 3-manifolds and -bundles over them including all rational homology spheres. These versions are analogous to the four flavors of monopole and Heegaard Floer homology theories. This construction…
Proposes SE(3) equivariant graph neural networks with local frames for efficient geometric approximation.
problem Equivariance in deep learning for arbitrary transformations, especially in physics.
method Introduces SE(3) equivariant graph neural networks with complete local frames to efficiently approximate geometric quantities.
result Achieves best or competitive performance in Newton mechanics modeling and equilibrium molecule conformation generation.
We give a construction of cyclic cocycles representing the equivariant characteristic classes of equivariant bundles. Our formulas generalize Connes' Godbillon-Vey cyclic cocycle. An essential tool of our construction is Connes-Moscovici's theory of cyclic cohomology of Hopf algebras.
Defines an equivariant Ruelle dynamical zeta function for flows on manifolds.
problem Defining a zeta function for equivariant flows on manifolds.
method Equivariant generalization of Guillemin's trace formula.
result Computes the equivariant Ruelle zeta function in various examples.
In this short note we prove an equivariant version of the formality of multidiffirential operators for a proper Lie group action. More precisely, we show that the equivariant Hochschild-Kostant-Rosenberg quasi-isomorphism between the cohomology of the equivariant multidifferential operators and the complex of equivaria…
We construct the odd symplectic structure and the equivariant even (pre)symplectic one from it on the space of differential forms on the Riemann manifold. The Poincare -- Cartan like invariants of the second structure define the equivariant generalizations of the Euler classes on the surfaces.
We present three equivalent definitions of -equivariant symplectic homology. We show that, using rational coefficients, the positive part of -equivariant symplectic homology is isomorphic to linearized contact homology, when the latter is defined. We present several computations and applications, and introduc…
New minimal hypersphere found in 4-sphere solving Bernstein problem.
problem Spherical Bernstein problem in
method Equivariant min-max theory for -invariant minimal hypersurfaces
result Construction of embedded non-equatorial minimal hypersphere
We refine the intersection product in homology to an equivariant setting, which unifies several known constructions. As an application, we give a common generalisation of the Chas-Sullivan string product on a manifold and the Chataur-Menichi string product on the classifying space by defining a string product on the Bo…
Develops a new method for equivariant Lagrangian Floer homology using symplectic homotopy quotients.
problem Constructing equivariant Lagrangian Floer homology for symplectic manifolds with group actions.
method Using symplectic homotopy quotients involving cotangent bundles of an approximation of , and Wehrheim and Woodward's theory of quilts.
result Shows that the constructed groups are independent of auxiliary choices and are -bimodules.
The paper generalizes equivariant neural networks on homogeneous spaces to the non-linear setting.
problem Equivariant neural networks on homogeneous spaces.
method Deriving generalized steerability constraints for non-linear equivariant layers.
result The universality of the derived construction for non-linear equivariant layers.
We construct Bott-type and stable equivariant Seiberg-Witten Floer homology and cohomology for rational homology spheres, and prove their diffeomorphism invariance.
New method finds Lie group representations without explicit groups, enabling new neural network architectures.
problem Building neural networks equivariant to arbitrary Lie groups.
method Algorithm to find Lie group representations from Lie algebra structure constants. Self-contained method for constructing Lie group-equivariant neural networks.
result First object-tracking model equivariant to the Poincaré group.