The paper introduces the spirality character of the almost fiber part for a closed essentially immersed subsurface of a closed orientable aspherical 3-manifold, which generalizes an invariant due to Rubinstein and Wang. The subsurface is virtually embedded if and only if the almost fiber part is aspiral, and in this ca…
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48 results for “invariant subsurfaces”
The study finds abundant normal generators for mapping class groups.
problem Understanding normal generation in mapping class groups.
method Analyzing restrictions on invariant subsurfaces and Teichmüller spaces.
result Reducible mapping classes can normally generate mapping class groups based on their asymptotic translation lengths.
The article studies Hamiltonian flows on surface group representations induced by invariant multi-functions.
problem Hamiltonian flows on surface group representations induced by invariant multi-functions.
method Introducing subsurface deformation and proving Poisson commutativity of induced invariant multi-functions.
result Hamiltonian flows on character varieties are of subsurface deformation type and Poisson commute if supporting subsurfaces are disjoint.
Formula for projecting geodesics in hyperbolic 3-manifolds, relating lengths to subsurface projections.
problem Relating lengths of geodesics to projections in hyperbolic 3-manifolds.
method Formula with explicit constants relating subsurface projections to geodesic lengths.
result Effective and computable large projections versus short curves relation.
On each nonorientable surface of odd genus , we give a mapping class whose dilatation on an invariant subsurface is the golden ratio.
We prove a continuity property for ending invariants of convergent sequences of Kleinian surface groups. We also analyze the bounded curve sets of such groups and show that their projections to non-annular subsurfaces lie a bounded Hausdorff distance from geodesics joining the projections of the ending invariants.
Random subsurfaces of hyperbolic surfaces equidistribute to ribbon graphs.
problem Distribution of shapes of complementary subsurfaces in moduli space.
method Study of shapes of complementary subsurfaces in moduli space as boundary lengths go to infinity.
result Random subsurfaces look like random ribbon graphs.
The contraction of the image of the Johnson homomorphism is called the Chillingworth class. In this paper, we derive a combinatorial description of the Chillingworth class for Putman's subsurface Torelli groups. We also prove the naturality and uniqueness properties of the map whose image is the dual of the Chillingwor…
Study on compact and finite-type support in mapping class group homology.
problem Understanding non-trivial classes supported on compact or finite-type subsurfaces.
method Use of shiftable subsurfaces and homological stability for finite-type surfaces.
result Almost-complete answer for surfaces with positive genus, partial answer for zero genus.
This expository article discusses some connections between the geometry of a hyperbolic 3-manifold homotopy-equivalent to a surface, and the combinatorial properties of its end invariants. In particular a necessary and sufficient condition is stated for the manifold to have arbitrarily short geodesics, in terms of a se…
Efficiently quantifies uncertainty in subsurface flow using neural networks guided by theory.
problem Uncertainty in dynamic subsurface flow predictions.
method Theory-guided Neural Network (TgNN) for efficient uncertainty quantification.
result TgNN surrogate improves efficiency of uncertainty quantification compared to MC method.
Sequential geophysical and flow inversion to characterize fracture networks in subsurface systemscs.CE
Subsurface applications including geothermal, geological carbon sequestration, oil and gas, etc., typically involve maximizing either the extraction of energy or the storage of fluids. Characterizing the subsurface is extremely complex due to heterogeneity and anisotropy. Due to this complexity, there are uncertainties…
SAGE generates subsurface velocity models from sparse well logs and seismic images.
problem Lack of high-quality subsurface velocity models due to limited data availability.
method Subsurface AI-driven geostatistical extraction using proxy posterior.
result SAGE produces geologically plausible and statistically accurate velocity realizations.
Congruence Subgroup Property for nilpotent groups and subsurface subgroups of Mapping Class Groupsmath.GR
Proves Congruence Subgroup Property for two types of groups.
problem Proving Congruence Subgroup Property for specific groups.
method Elementary proof of Johnson filtration and geometric subsurface inclusions.
result Proves Congruence Subgroup Property for nilpotent quotients and subsurface subgroups.
Study arcs on surfaces, focusing on topological aspects and group actions.
problem Understanding arcs and their complements on surfaces.
method Characterize infinite-type surfaces via homeomorphic subsurfaces, construct actions on arc graphs.
result New characterisation of infinite-type surfaces and actions on arc graphs.
Combines deep generative models with ensemble methods for subsurface property estimation.
problem Estimating spatially distributed subsurface properties from sparse measurements.
method Wasserstein Generative Adversarial Network (WGAN-GP) and Ensemble Smoother with Multiple Data Assimilation (ES-MDA).
result The proposed method outperforms variational inversion methods, especially for channelized and fractured fields.
We introduce a method for constructing Weil-Petersson (WP) geodesics with certain behavior in the Teichmüller space. This allows us to study the itinerary of geodesics among the strata of the WP completion and its relation to subsurface projection coefficients of their end invariants. As an application we demonstrate t…
The paper introduces a new differential-geometric system which originates from the theory of -Hessian operators. The core of this system is a new notion of invariant differentiation on multidimensional surfaces. This novelty gives rise to the following absolute geometric invariants: invariant derivatives of the surf…
This paper is a study of the subgroups of the mapping class groups of Riemann surfaces, called "geometric" subgroups, corresponding to the inclusion of subsurfaces. Our analysis includes surfaces with boundary and with punctures. The centres of all the mapping class groups are calculated. We determine the kernel of inc…
Let M be a surface (possibly nonorientable) with punctures and/or boundary components. The paper is a study of ``geometric subgroups'' of the mapping class group of M, that is subgroups corresponding to inclusions of subsurfaces (possibly disconnected). We characterise the subsurfaces which lead to virtually abelian ge…
We give a simple criterion for a Heegaard splitting to yield a Haken manifold. As a consequence, we construct many Haken manifolds, in particular homology spheres, with prescribed properties, namely Heegaard genus, Heegaard distance and Casson invariant. Along the way we give simpler and shorter proofs of the existence…
We compare the flat geometry associated to a quadratic differential with the hyperbolic geometry associated to the underlying Riemann surface. We show that if a curve is contained in a thick subsurface, then its hyperbolic length is comparable to its flat length times the flat size of the subsurface.
Study shows surfaces without certain curves have infinite orbit graph.
problem Characterizing surfaces with specific curve properties.
method Utilized tools from mapping class group geometry.
result Infinite-invariance index 1 surfaces lack good curve graphs.
New projection complex shows some surface homeomorphisms have positive commutator length.
problem Understanding commutator length in surface homeomorphisms.
method Constructing unbounded quasi-trees and a new projection complex.
result Some surface homeomorphisms have positive stable commutator length.
This paper has two main goals. First, we give a complete, explicit, and computable solution to the problem of when two simple closed curves on a surface are equivalent under the Johnson kernel. Second, we show that the Johnson filtration and the Johnson homomorphism can be defined intrinsically on subsurfaces and prove…
We study the connections between subsurface projections in curve and arc complexes in fibered 3-manifolds and Agol's veering triangulation. The main theme is that large-distance subsurfaces in fibers are associated to large simplicial regions in the veering triangulation, and this correspondence holds uniformly for all…
New graphs show hierarchical hyperbolic properties, extending previous work.
problem Characterizing hierarchically hyperbolic properties of multiarc and curve graphs.
method Analyzing the geometric intersection number and using PMod(S) action.
result Multiarc and curve graphs are hierarchically hyperbolic.
Study classifies mapping class groups with hyperbolic actions on infinite-type surfaces.
problem Classifying mapping class groups with hyperbolic actions on infinite-type surfaces.
method Analyzing curve graphs and their translates to construct hyperbolic spaces.
result Classification of mapping class groups with hyperbolic actions.
Graphs of multicurves are hyperbolic, relatively hyperbolic, or thick.
problem Characterizing graphs of multicurves based on their geometric properties.
method Proving graphs of multicurves are hyperbolic, relatively hyperbolic, or thick based on subsurface intersections.
result Geometric characterization of graphs of multicurves.
A Critical Review of Physics-Informed Machine Learning Applications in Subsurface Energy Systemscs.LG
PIML enhances machine learning for subsurface energy systems.
problem Lack of interpretability and domain-specific knowledge in machine learning models.
method Integrates physics principles into data-driven models using deep learning.
result PIML improves model generalization and adherence to physical laws.
SURGIN uses generative models to infer subsurface flow data efficiently.
problem Inefficient and task-specific inversion methods for subsurface multiphase flow.
method SURGIN integrates U-FNO surrogate with SGM for zero-shot conditional generation.
result Decent inference of heterogeneous geological fields and flow dynamics with uncertainty quantification.
We show that the subsurface projection of a train track splitting sequence is an unparameterized quasi-geodesic in the curve complex of the subsurface. For the proof we introduce induced tracks, efficient position, and wide curves. This result is an important step in the proof that the disk complex is Gromov hyperbolic…
Proves conjecture about surface cover homology.
problem Proving Putman-Wieland conjecture about surface covers.
method Analyzes homology classes of curves and subsurfaces.
result Generates homology of covers by specific curve lifts.
Uniform bound on geodesic images for surfaces using bicorn curves.
problem Bounding geodesic images on closed surfaces.
method Utilizing bicorn curves and properties of 1-slim triangles.
result Uniform bound of 44 for non-annular subsurfaces, 3 for specific cases.
Garside-theoretical solutions to the conjugacy problem in braid groups depend on the determination of a characteristic subset of the conjugacy class of any given braid, e.g. the sliding circuit set. It is conjectured that, among rigid braids with a fixed number of strands, the size of this set is bounded by a polynomia…
By Torelli topology the author understands aspects of the topology of surfaces (potentially) relevant to the study of Torelli groups. The extension problem in Torelli topology is the problem of determining when a diffeomorphism of compact connected subsurface of a closed surface can be extended to a diffeomorphism of t…
We give a new proof of a celebrated theorem of Dennis Johnson that asserts that the kernel of the Johnson homomorphism on the Torelli subgroup of the mapping class group is generated by separating twists. In fact, we prove a more general result that also applies to "subsurface Torelli groups". Using this, we extend Joh…
Deep Learning of Dynamic Subsurface Flow via Theory-guided Generative Adversarial Networkphysics.geo-ph
Tackles dynamic subsurface flow via GAN with physical theory constraints.
problem Deep learning of dynamic subsurface flow with heterogeneous parameters.
method Theory-guided generative adversarial network (TgGAN) for PDEs.
result TgGAN predicts future subsurface flow responses robustly and efficiently.
In this paper, by putting a separating incompressible surface in a 3-manifold into Morse position relative to the height function associated to a strongly irreducible Heegaard splitting, we show that an incompressible subsurface of the Heegaard splitting can be found, by decomposing the 3-manifold along the separating …
We examine the internal geometry of a Kleinian surface group and its relations to the asymptotic geometry of its ends, using the combinatorial structure of the complex of curves on the surface. Our main results give necessary conditions for the Kleinian group to have `bounded geometry' (lower bounds on injectivity radi…
Develops active intervals for geodesics in Teichmüller space.
problem Understanding geodesics in Teichmüller space with no backtracking.
method Defines active intervals for subsurfaces along geodesics in Thurston metric.
result Active intervals represent reparametrized quasi-geodesics in curve graphs with bounded movement outside.
Growth rates of geodesics on modular orbifolds are studied.
problem Understanding growth rates of geodesics on modular orbifolds.
method Exhaustion of modular orbifold by compact subsurfaces, analysis of low lying geodesics and reciprocal geodesics.
result Growth rates of low lying geodesics and reciprocal geodesics converge to the full set's growth rate.
The curve graphs are not locally finite. In this paper, we show that the curve graphs satisfy a property which is equivalent to graphs being uniformly locally finite via Masur--Minsky's subsurface projections. As a direct application of this study, we show that there exist computable bounds for Bowditch's slices on tig…
Deep learning methods improve subsurface flow modeling efficiency.
problem Efficiently modeling subsurface flow with uncertain parameters.
method Two categories of deep-learning based inverse modeling methods: surrogate-based and direct.
result Deep-learning methods significantly accelerate subsurface flow modeling.
Study of homeomorphisms on infinite type surfaces with a classification theorem.
problem Classifying homeomorphisms on surfaces of infinite type.
method Introduce tame homeomorphisms and prove a Nielsen-Thurston type classification theorem.
result For tame homeomorphisms, surfaces decompose into invariant subsurfaces with canonical decompositions.
Study on random surfaces in hyperbolic 3-manifolds, focusing on geometric and topological properties.
problem Distribution of nearly geodesic surfaces in hyperbolic 3-manifolds.
method Invariant measures on the Grassmann bundle G(M) derived from limits of random minimal surfaces.
result Topological limiting measures are totally scarring if M contains a totally geodesic subsurface, while geometrical limiting measures are not.
Johnson kernel generated by specific Dehn twists on surfaces.
problem Identifying the generating set of Johnson kernel for surfaces.
method Analyzing Dehn twists on specific types of surfaces.
result Johnson kernel generated by Dehn twists on specified surfaces.
Let be a smooth connected compact surface and be either a real line or a circle. This paper proceeds the study of the stabilizers and orbits of smooth functions on with respect to the right action of the group of diffeomorphisms of . A large class of smooth maps with isolated singularities is …