Proves isomorphism conjecture for braid groups.
problem Proving isomorphism conjecture for braid groups.
method Fibered Isomorphism Conjecture of F. T. Farrell and L. E. Jones.
result Proved and theoretic versions of the conjecture.
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48 results for “Fibered Isomorphism Conjecture”
We prove the Farrell-Jones fibered isomorphism conjecture for several classes of Artin groups of finite and affine types. As a consequence, we compute explicitly the surgery obstruction groups of the finite type pure Artin groups.
In this paper we show that the fibered isomorphism conjecture of Farrell and Jones corresponding to the stable topological pseudoisotopy functor is true for the fundamental groups of a large class of complex manifolds. A consequence of this result is that the Whitehead group, reduced projective class groups and the neg…
We study the Fibered Isomorphism Conjecture of Farrell and Jones in L-theory for groups acting on trees. In several cases we prove the conjecture. This includes wreath products of abelian groups and free metabelian groups. We also deduce the conjecture in pseudoisotopy theory for these groups. Finally in B of Theorem 1…
In this article we study the K- and L-theory of groups acting on trees. We consider the problem in the context of the fibered isomorphism conjecture of Farrell and Jones. We show that in the class of residually finite groups it is enough to prove the conjecture for finitely presented groups with one end. Also, we deduc…
This is the first of three articles on the Fibered Isomorphism Conjecture of Farrell and Jones for L-theory. We apply the general techniques developed in [15] and [16] to the L-theory case of the conjecture and prove several results. Here we prove the conjecture, after inverting 2, for poly-free groups. In particular, …
In this short note we prove that the Farrell-Jones Fibered Isomorphism Conjecture in L-theory, after inverting 2, is true for a group whose some derived subgroup is free.
We study the Fibered Isomorphism conjecture of Farrell and Jones for groups acting on trees. We show that under certain conditions the conjecture is true for groups acting on trees when the stabilizers satisfy the conjecture. These conditions are satisfied in several cases of the conjecture. We prove some general resul…
Topological models confirmed for Springer fibers of even orthogonal and symplectic groups.
problem Understanding the topology of Springer fibers for even orthogonal and symplectic groups.
method Explicit construction of topological models and proving homeomorphism to Springer fibers.
result Springer fibers for even orthogonal and symplectic groups are homeomorphic to their topological models.
We prove similar theorems concerning the structure of bundles involving complements of fiber-type hyperplane arrangements and orbit configuration spaces. These results facilitate analysis of the fundamental groups of these spaces, which may be viewed as generalizations of the Artin pure braid group. In particular, we r…
The Farrell-Jones Fibered Isomorphism Conjecture for the stable topological pseudoisotopy theory has been proved for several classes of groups. For example for discrete subgroups of Lie groups, virtually poly-infinite cyclic groups, Artin braid groups, a class of virtually poly-surface groups and virtually solvable lin…
New exotic 4-manifolds found with fiber bundles.
problem Finding non-diffeomorphic exotic 4-manifolds.
method Smooth fiber bundles over the circle.
result Exotic 4-manifolds with non-simply-connected fiber.
Using a recent result of Bartels and Lueck (arXiv:0901.0442) we deduce that the Farrell-Jones Fibered Isomorphism conjecture in L-theory is true for any group which contains a finite index strongly poly-free normal subgroup, in particular, for the Artin full braid groups. As a consequence we explicitly compute the surg…
In this paper we generalize the notion of strongly poly-free group to a larger class of groups, we call them strongly poly-surface groups and prove that the Fibered Isomorphism Conjecture of Farrell and Jones corresponding to the stable topological pseudoisotopy functor is true for any virtually strongly poly-surface g…
The isomorphism conjecture for 3-manifold groups and K-theory of virtually poly-surface groupsmath.KT
This article has two purposes. In \cite{R3} (math.KT/0405211) we showed that the FIC (Fibered Isomorphism Conjecture for pseudoisotopy functor) for a particular class of 3-manifolds (we denoted this class by \cal C) is the key to prove the FIC for 3-manifold groups in general. And we proved the FIC for the fundamental …
Fibered Correspondencemath.DG
Base of fibered correspondence is arbitrary correspondence. Fibered correspondence is interesting when we consider relationship between different bundles. However composition of fibered correspondences may not always be defined. Reduced fibered correspondence is defined only between fibers over the same point of base. …
Paper shows 3D hyperbolic manifolds are uniquely identified by their finite groups.
problem Identifying hyperbolic 3-manifolds using their finite quotient groups.
method Proves profinite isomorphism of fundamental groups uniquely determines the manifold's isomorphism type.
result Finite-volume hyperbolic 3-manifolds are almost determined by their finite quotient groups.
Study Turaev-Viro invariants of Seifert fibered 3-manifolds, proving volume conjecture.
problem Understanding the asymptotic behavior of Turaev-Viro invariants for Seifert fibered 3-manifolds.
method Analysis of large asymptotic behavior of Turaev-Viro invariants.
result Proved the volume conjecture for Seifert fibered 3-manifolds with empty and non-empty boundaries.
Study of Seifert fibered spaces using surface complexes.
problem Understanding the topology of Seifert fibered spaces.
method Defined surface complex for 3-manifolds, applied to Seifert fibered spaces.
result Surface complex of Seifert fibered spaces contains a subcomplex isomorphic to the curve complex of the base orbifold.
We describe explicit open books on arbitrary plumbings of oriented circle bundles over closed oriented surfaces. We show that, for a non-positive plumbing, the open book we construct is horizontal and the corresponding compatible contact structure is also horizontal and Stein fillable. In particular, we describe horizo…
Artin groups have a special structure that helps prove a complex mathematical conjecture.
problem Proving the Farrell-Jones isomorphism conjecture for Artin groups.
method Identifying an inductive structure in Artin groups and applying it to the conjecture.
result The Farrell-Jones isomorphism conjecture is proven for certain Artin groups.
Study Veech groups in fibered 3-manifolds, proving no parabolics for fibers.
problem Characterizing Veech groups in fibered 3-manifolds.
method Analyzing pseudo-Anosov monodromies and foliations, proving properties of Veech groups.
result Veech groups in fibers typically contain no parabolic elements.
The paper studies Kobayashi pseudometric, complex automorphisms, and hyperkaehler manifolds.
problem Characterizing automorphisms and pseudodistances on complex manifolds.
method Defining Kobayashi quotient, proving isomorphisms, and analyzing pseudodistances.
result Proves Kobayashi's conjecture on hyperkaehler manifolds and automorphisms.
We prove new results about unknotting fibered positive knots and braids.
problem Proving the unknotting number equals genus for fibered positive knots and braids.
method Analyzing positive braid diagrams and fibered positive knots, proving new constraints and conjectures.
result We found fibered positive knots that cannot be unknotted optimally, contradicting Stoimenow's conjecture.
Extends Frohman and Rannard's result to Seifert fiber spaces with singular surfaces.
problem Characterize essential surfaces in Seifert fiber spaces with singular surfaces.
method Extends Frohman and Rannard's approach to handle surfaces with singular fibers.
result Characterizes essential surfaces in Seifert fiber spaces with singular surfaces.
Akbulut and Kirby conjectured that two knots with the same -surgery are concordant. In this paper, we prove that if the slice-ribbon conjecture is true, then the modified Akbulut-Kirby's conjecture is false. We also give a fibered potential counterexample to the slice-ribbon conjecture.
The paper studies Kähler-Einstein metrics on fiber spaces with positive Kodaira dimension.
problem Understanding Kähler-Einstein metrics on fiber spaces with positive Kodaira dimension.
method Analyzes the properties of singular Kähler-Einstein metrics and their curvature.
result The fiberwise singular Kähler-Einstein metric induces a semipositively curved metric on the relative canonical bundle.
We compute the -equivariant Seiberg-Witten Floer homology of Seifert rational homology three-spheres in terms of their Heegaard Floer homology. As a result of this computation, we prove Manolescu's conjecture that for Seifert integral homology three-spheres. We show that the Manolescu invari…
Using contact surgery we define families of contact structures on certain Seifert fibered three-manifolds. We prove that all these contact structures are tight using contact Ozsath-Szabo invariants. We use these examples to show that, given a natural number n, there exists a Seifert fibered three-manifold carrying at l…
Paper solves Hilbert's fifth problem for specific groupoids.
problem When are transitive groupoids continuously isomorphic to Lie groupoids?
method Investigates proper and transitive groupoids with compact source fibers.
result Solves Hilbert's fifth problem for specified groupoids.
The paper studies fibers of maps in totally nonnegative spaces.
problem Understanding the structure of fibers of Chevalley exponentiation maps.
method Cell stratifications, face posets, and homeomorphic CW complexes.
result Fibers are homeomorphic to interior dual block complexes of subword complexes.
The paper extends Hilbert's fifth problem to transitive groupoids.
problem When is a transitive topological groupoid continuously isomorphic to a Lie groupoid?
method Investigation of transitive topological groupoids, focusing on proper and transitive groupoids with compact source fibers.
result Presentation of results generalizing Hilbert's fifth problem to transitive groupoids, including solutions for proper and transitive groupoids with compact source fibers.
Constructs special Lagrangian submanifolds in Calabi-Yau 3-folds.
problem Constructing special Lagrangian submanifolds in collapsing Calabi-Yau 3-folds.
method Constructs special Lagrangian submanifolds in collapsing Calabi-Yau 3-folds fibered by K3 surfaces.
result Special Lagrangian submanifolds shrink to 1-dimensional graphs in the base as the 3-folds collapse.
Classifies genus-1 holomorphic Lefschetz pencils up to smooth isomorphism.
problem Classifying genus-1 holomorphic Lefschetz pencils up to smooth isomorphism.
method Analyzes pencils on and of specific degrees, determines monodromy factorizations, and classifies blow-ups.
result Classifies pencils on and of specific degrees up to smooth isomorphism.
Sharp knots and iterated cables lead to ribbon knots or failure of slice-ribbon conjecture.
problem Understanding the concordance properties of knots and their cables.
method Using Seifert genus and concordance invariant γ0 from bordered Heegaard Floer homology.
result Connected sums of γ0-sharp fibered knots are ribbon only if they are of a specific form, or the slice-ribbon conjecture fails.
Researchers prove a conjecture linking 1-loop invariants to torsion for fibered 3-manifolds.
problem Proving a conjecture about polynomial invariants and torsion for fibered 3-manifolds.
method Using combinatorial data of ideal triangulations and layered triangulations of fibered 3-manifolds with toroidal boundary, proving the conjecture for specific cases and confirming it for a large number of nonfibered manifolds.
result The conjecture linking 1-loop invariants to torsion for fibered 3-manifolds with toroidal boundary is proven.
Study Turaev-Viro invariants of 3-manifolds with toroidal boundary.
problem Volume conjecture for Seifert fibered and graph 3-manifolds.
method Large asymptotic behavior of Turaev-Viro invariants under gluing operation.
result Volume conjecture proven for Seifert fibered and graph 3-manifolds.
New method determines arrangement combinatorics from Milnor fiber boundary.
problem Determining arrangement combinatorics from Milnor fiber boundary.
method Explicit method using plumbing graph in normal form.
result Milnor fiber boundary determines arrangement combinatorics.
We show that the Fibered Isomorphism Conjecture (FIC) of Farrell and Jones corresponding to the stable topological pseudoisotopy functor is true for the fundamental groups of a large class of 3-manifolds. We also prove that if the FIC is true for irreducible 3-manifold groups then it is true for all 3-manifold groups. …
New techniques compute -cohomology of quasi-fibered metrics.
problem Compute -cohomology of quasi-fibered boundary metrics.
method Developed new techniques to compute weighted -cohomology.
result Computed reduced -cohomology for various classes of QFB-metrics.
Either fibered knots supporting the tight contact structure are unique in their smooth concordance class or there exists a fibered counterexample to the Slice-Ribbon Conjecture.
The Upsilon invariant helps classify fibered knots and their open book decompositions.
problem Classifying fibered knots and their open book decompositions.
method Using the Ozsváth-Stipsicz-Szabó concordance invariant Upsilon.
result Fibered knots satisfying a specific condition are either unique in their smooth concordance classes or provide counterexamples to the Slice-Ribbon Conjecture.
The Milnor fiber conjecture is proven for splice type singularities.
problem Proving the Milnor fiber conjecture for a specific class of singularities.
method Combining techniques from tropical geometry, log geometry, and rounding of logarithmic spaces.
result The Milnor fiber conjecture is proven for splice type singularities.
The main result of this paper, Simon's conjecture for fibered knots, was previously proven by Silver and Whitten math.GT/0405462 with essentially the same proof. This paper is therefore being withdrawn. The author would like to apologize for having missed this.
The paper proves a precise SYZ conjecture for toric Calabi-Yau manifolds with singular fibers.
problem Proving the SYZ conjecture for Calabi-Yau manifolds with singular fibers.
method Using family Floer mirror construction and Gross Lagrangian fibration.
result The dual singular fibration is compatible with the family Floer mirror construction.
Counterexample disproves conjecture on flat metrics and fiber bundles.
problem Conjecture about flat metrics and fiber bundles on manifolds.
method Study of transversely flat Riemannian foliations.
result Found a counterexample to the conjecture.
The article provides formulas for homological blocks of Seifert fibered homology 3-spheres.
problem Calculating Witten-Reshetikhin-Turaev invariants for Seifert fibered homology 3-spheres.
method Explicit modular transformation formulas of homological blocks.
result New proof of Witten asymptotic conjecture for Seifert fibered homology 3-spheres.
New examples show not all homology fiber bundles are topological.
problem Disprove conjecture about homology fiber bundles.
method Construct flat, projective morphisms that are -homology fiber bundles.
result Disprove conjecture about homology fiber bundles.