Paper explains dynamics of homeomorphisms to mapping tori geometry.
problem Understanding dynamics of end-periodic homeomorphisms.
method Illustration-driven overview of recent results.
result Analogue of Brock's theorem for infinite-type surfaces.
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48 results for “end-periodic mapping tori”
Embeddings of mapping tori for end-periodic graph maps are proven.
problem Embedding mapping tori of end-periodic graph maps into finite complexes.
method Flowline-preserving homotopy equivalence and -injective map.
result Every mapping class of Γ arising from an end-periodic homotopy equivalence contains a representative whose mapping torus realizes such an embedding.
Lower bound on volumes of special mapping tori.
problem Calculating the minimum volume of compactified mapping tori.
method Using strongly irreducible end-periodic homeomorphisms and properties of pants graphs.
result Volume of compactified mapping tori is comparable to the translation length of the homeomorphism on pants graphs.
This research studies end-periodic mapping tori and their hyperbolic structures.
problem Understanding the geometry and dynamics of end-periodic mapping tori.
method Analyzes invariant laminations and hyperbolic structures of mapping tori.
result Establishes a relationship between the geodesic length of boundary components and the infimum of geodesic lengths in hyperbolic structures.
Upper bound on 3-manifold volumes from surface homeomorphisms.
problem Bounding volumes of 3-manifolds from surface homeomorphisms.
method Using end-periodic homeomorphisms and pants graphs.
result Upper bound on infimal hyperbolic volume is asymptotically sharp.
Lower bound on stretch factor for periodic maps.
problem Finding a lower bound on stretch factors for periodic maps.
method Using core characteristic of end-periodic homeomorphisms, we derive a lower bound on the Handel-Miller stretch factor.
result The derived bound is sharp and measures topological complexity.
Derives an index formula for families of end-periodic Dirac operators.
problem Calculating the index of families of end-periodic Dirac operators.
method Using the renormalized Chern character and Fourier-Laplace transform of the Bismut superconnection.
result Establishes an index formula involving a new end-periodic eta form.
The paper generalizes index theory for periodic manifolds and proves equivalence of signatures for tori.
problem Generalizing index theory for periodic manifolds and proving signature equivalence for tori.
method Periodic index theory and spectral flow for elliptic complexes, surgery formula for singular instanton homology.
result Equivalence of signatures for essentially embedded tori and surgery formula for singular instanton homology.
Every weak Perron number is realized as a stretch factor of a homeomorphism on a surface.
problem Finding stretch factors for weak Perron numbers.
method Constructing an end-periodic homeomorphism on a surface.
result Every weak Perron number is an end-periodic stretch factor.
This paper studies Dirac operators on end-periodic spin manifolds of dimension at least 4. We provide a sufficient condition for such an operator to be Fredholm for a generic end-periodic metric; this condition is shown to be necessary in dimension 4. We make use of end-periodic Dirac operators to give an analytical in…
By studying the Seiberg-Witten equations on end-periodic manifolds, we give an obstruction on the existence of positive scalar curvature metric on compact -manifolds with the same homology as . This obstruction is given in terms of the relation between the Frøyshov invariant of the generator of $H…
We obtain two types of results on positive scalar curvature metrics for compact spin manifolds that are even dimensional. The first type of result are obstructions to the existence of positive scalar curvature metrics on such manifolds, expressed in terms of end-periodic eta invariants that were defined by Mrowka-Ruber…
Classifies mapping tori of specific groups, generalizing known results.
problem Classifying mapping tori of specific groups.
method Using Hopf-type properties and Poincaré Duality groups.
result Generalizes and provides new proofs for fibered 3-manifolds.
New findings on isospectral tori and harmonic maps between flat tori.
problem Determining if isospectral tori are isometric using harmonic maps.
method Examined harmonic maps between flat tori, focusing on Milnor's isospectral tori.
result Milnor's isospectral tori cannot be distinguished by harmonic maps from lower-dimensional tori, but can be distinguished by higher-dimensional ones.
New non-Kähler examples of generalized Kähler manifolds constructed via mapping tori.
problem Constructing new non-Kähler generalized Kähler manifolds.
method Starting from a 3-torus and a compact Kähler manifold, constructing via mapping tori.
result Obtained new non-Kähler examples and recovered known examples of generalized Kähler solvmanifolds.
We extend the Atiyah, Patodi, and Singer index theorem for first order differential operators from the context of manifolds with cylindrical ends to manifolds with periodic ends. This theorem provides a natural complement to Taubes' Fredholm theory for general end-periodic operators. Our index theorem is expressed in t…
The study characterizes subgroups of mapping tori of free groups.
problem Characterizing subgroups of mapping tori of free groups.
method Using canonical maximal sub-mapping tori and relative hyperbolicity.
result Characterizes locally quasi-convex hyperbolic groups.
Minimal volume entropy vanishes for mapping tori over 3-manifolds.
problem Volume entropy of mapping tori over 3-manifolds.
method A variation of amenable category and minimal volume entropy of a homology class.
result Minimal volume entropy vanishes.
Free maps exist on low-dimensional tori and closed surfaces.
problem Embedding closed surfaces in high-dimensional spaces.
method Factorization trick for constructing free immersions.
result Every closed surface embeds freely in \(\mathbb{R}^5\).
Study on spectral points of Inoue surfaces with Tricerri metric.
problem Identifying spectral points on Inoue surfaces.
method Analyzing chiral Dirac operators twisted by flat -connections.
result No spectral points inside the annulus , with spectral points on boundary.
We survey the interactions between foliations and contact structures in dimension three, with an emphasis on sutured manifolds and invariants of sutured contact manifolds. This paper contains two original results: the fact that a closed orientable irreducible 3-manifold M with nonzero second homol-ogy carries a hyperti…
Integral filling volume, complexity and integral simplicial volume of 3-dimensional mapping torimath.GT
Integral filling volume of mapping tori grows sublinearly with complexity.
problem Characterizing mapping classes with vanishing integral filling volume.
method Analyzing Dehn twists and mapping tori, using simplicial volume and complexity.
result Integral simplicial volume of mapping tori grows sublinearly with respect to the monodromy power.
Homology growth of specific mapping tori vanishes for certain groups.
problem Homology growth of polynomially growing mapping tori in various groups.
method Proof of the cheap rebuilding property for specific groups.
result Torsion homology growth vanishes for Farber sequences in every degree.
On positive scalar curvature cobordisms and the conformal Laplacian on end-periodic manifoldsmath.DG
We show that the periodic -invariants introduced by Mrowka--Ruberman--Saveliev~\cite{MRS3} provide obstructions to the existence of cobordisms with positive scalar curvature metrics between manifolds of dimensions and . The proof combines a relative version of the Schoen--Yau minimal surface technique with an…
New construction method for special geometric structures.
problem Creating strong HKT and generalized hyperkähler structures.
method Mapping tori construction of skew-symmetric torsion.
result Non-product structures with parallel skew-symmetric torsion.
Researchers calculate dimensions of skein modules for 2-torus mapping tori.
problem Determining dimensions of Kauffman bracket skein modules for specific cases.
method Using generic and decomposing twisted Hochschild homology of -skein algebras.
result Dimensions of skein modules for and are calculated.
Researchers compute dimensions of GLN-skein modules for genus-one mapping tori.
problem Computing dimensions of GLN-skein modules for mapping tori.
method Explicit Euler product expansion of the skein partition function.
result Explicit computation of dimensions and generating function.
Proves conjecture for hyperbolic-by-cyclic groups using geometric methods.
problem Proving Farrell-Jones Conjecture for specific group structures.
method Geometric methods and structure theory of mapping tori.
result Proved Farrell-Jones Conjecture for mapping tori of automorphisms of hyperbolic-by-cyclic groups.
New theorem on flat tori stability using harmonic maps and Ricci flow.
problem Stability of flat tori under Ricci and scalar curvature bounds.
method Harmonic map heat flow, Ricci flow, and RCD theories.
result Gromov-Hausdorff stability theorem for flat 3-tori.
Study bounds topological entropy of maps on surfaces with punctures based on mapping torus homology.
problem Relating topological entropy of pseudo-Anosov maps to homology of mapping tori.
method Analyzing the topological entropy of pseudo-Anosov maps on surfaces with punctures and relating it to the rank of the first homology of their mapping tori.
result Entropy of a pseudo-Anosov map is bounded by a formula involving the genus, number of punctures, and homology rank.
New length functions on mapping class groups linked to simplicial volumes of mapping tori.
problem Understanding the relationship between mapping class groups and simplicial volumes of mapping tori.
method Introducing filling volumes as length functions and proving their properties.
result Real filling volumes equal the simplicial volume of mapping tori, while integral filling volumes are not smaller than the stable integral simplicial volume.
Maps from rational homology solid tori yield rank inequalities in Heegaard Floer homology.
problem Rank inequalities in Heegaard Floer homology.
method Using Hanselman-Rasmussen-Watson's bordered Floer homology, we extend their proof to rational homology solid tori.
result We provide rank inequalities for Heegaard Floer homology.
Study exotic tori and their SL_d(Z) actions, proving many do not admit nontrivial actions.
problem Characterize exotic tori admitting SL_d(Z) actions.
method Compute mapping class groups, analyze homology actions, and prove non-existence of nontrivial actions.
result Many exotic tori do not admit nontrivial SL_d(Z) actions.
New contact structures on folded sums of contact mapping tori are tight under certain conditions.
problem Understanding tight contact structures on folded sums of contact mapping tori.
method Alternative bundle-theoretical construction and gluing process near the fold.
result Folded contact structures on folded sums of contact mapping tori are tight under specific conditions.
We study random elements of subgroups (and cosets) of the mapping class group of a closed hyperbolic surface, in part through the properties of their mapping tori. In particular, we study the distribution of the homology of the mapping torus (with rational, integer, and finite field coefficients, the hyperbolic volume …
Non-coherence proven for certain groups with specific mapping tori.
problem Proving non-coherence for groups with specific mapping tori.
method Analyzing the structure of groups as extensions and properties of mapping tori.
result Groups with certain mapping tori are not coherent.
We show that the graph TQFT for Heegaard Floer homology satisfies a strong version of Atiyah's duality axiom for a TQFT. As an application, we compute some Heegaard Floer mixed invariants of 4-dimensional mapping tori in terms of Lefschetz numbers on .
We study a generalization of the familiar Poincaré map, first implicitely introduced by N.N. Nekhoroshev in his study of persistence of invariant tori in hamiltonian systems, and discuss some of its properties and applications. In particular, we apply it to study persistence and bifurcation of invariant tori.
The paper finds rotationally symmetric critical metrics for Laplace eigenvalues on tori.
problem Maximizing the first normalized Laplace-Beltrami eigenvalue on tori.
method Constructing equivariant harmonic maps to spheres and analyzing their properties.
result Rotationally symmetric critical metrics for the first eigenvalue are found and characterized.
We consider a random walk on the mapping class group of a surface of finite type. We assume that the random walk is determined by a probability measure whose support is finite and generates a non-elementary subgroup . We further assume that is not consisting only of lifts with respect to any one covering. Then w…
Authors create non-isometric 3-orbifolds with identical topology and volume.
problem Finding non-isometric hyperbolic 3-orbifolds with the same topological type and volume.
method Constructing pairs of non-isometric hyperbolic 3-orbifolds with the same topological type and volume.
result Demonstrated the existence of non-isometric hyperbolic 3-orbifolds with the same topological type and volume.
We prove that for every P there is a bound B depending only on P so that the mapping torus of every P--small irreducible train-track map can be obtained by surgery from one of B mapping tori. We show that given an integer P>0 there is a bound depending only on P, so that there exists a presentation of the fundament…
The aim of this paper is to show that Lawson's foliation on the 5-sphere admits a smooth leafwise symplectic structure. The main part of the construction is to show that the Fermat type cubic surface admits an end-periodic symplectic structure.
Pseudo-Anosov subgroups in surface bundles over tori are convex cocompact.
problem Understanding the structure of pseudo-Anosov subgroups in surface bundles over tori.
method Using the Birman exact sequence to show convex cocompactness.
result Finitely generated, purely pseudo-Anosov subgroups are convex cocompact in surface bundles over tori.
We prove that the conformal immersions of complex two tori into which locally minimize their conformal volume in their conformal class all satisfy some elliptic PDE. We prove that they are either minimal tori, CMC flat tori, elliptic conformally constrained minimal tori or critical point of the area under some fi…
New method constructs multi-monopoles on mapping tori.
problem Understanding wall-crossing in multi-monopole counts.
method Adiabatic limit theorem to construct multi-monopoles.
result First explicit constructions of multi-monopoles in various chambers.
The classical Fundamental Theorem of Affine Geometry states that for , any bijection of -dimensional Euclidean space that maps lines to lines (as sets) is given by an affine map. We consider an analogous characterization of affine automorphisms for compact quotients, and establish it for tori: A bijection o…
We show -type inequalities for some end-periodic -manifolds which have positive scalar curvature metrics on the ends. As an application, we construct a new family of closed -manifolds which do not admit positive scalar curvature metrics.