Study 2-loop part of Johnson cokernel using trace map.
problem Identify components of Johnson cokernel in degree 6.
method Use 2-loop trace map to capture Johnson cokernels.
result Capture all components of Johnson cokernels in degree 6.
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35 results for “cokernel”
In the present paper, we study the Sp-module structure of the cokernel of the Johnson homomorphism of the mapping class groups of surfaces. We detect the Sp-irreducible components with highest weight [1^k] (and [k]) in the cokernel. We also show that the multiplicities of them is equal to one.
Paper compares and intersects classes in Johnson cokernels of surface mapping groups.
problem Comparing and intersecting classes in Johnson cokernels of mapping class groups of surfaces.
method Representation theoretic and topological approaches.
result Anti-Morita obstructions and hook-type components appear in the Johnson cokernels.
The paper finds torsion in Johnson homomorphisms' cokernels for large genus surfaces.
problem Existence of torsion in the cokernels of Johnson homomorphisms.
method Defined a map on Ker(Tr)∩D(H) whose image is 2-torsion and vanishes on the image of τ.
result Found 2-torsion in the cokernels of Johnson homomorphisms for large genus surfaces.
We show that if H is a cocommutative Hopf algebra, then there is a natural action of Aut(F_n) on the nth tensor power of H which induces an Out(F_n) action on a quotient \overline{H^{\otimes n}}. In the case when H=T(V) is the tensor algebra, we show that the invariant Tr^C of the cokernel of the Johnson homomorphism s…
Study shows non-locally-flat concordance elements in knot theory.
problem Understanding non-locally-flat concordance elements in knot theory.
method Utilized Heegaard Floer homology.
result Cokernel of the map from smooth knot concordance group to homology concordance group is infinitely generated and contains elements of infinite order.
We present a version of the Penrose transform which relates compactly supported cohomology on a complex or CR manifold Z to kernels and cokernels of differential operators on a parameter space X of compact complex submanifolds of Z.
New method constructs solution operators for PDEs with prescribed support properties.
problem Constructing solution operators for under/overdetermined PDEs with specific support properties.
method Using a recovery on curves condition and taking smooth averages over curves, we obtain integral solution operators and representation formulas.
result Our method leads to integral representation formulas for overdetermined PDEs and solution operators for underdetermined PDEs.
We study the natural map eta between a group of binary planar trees whose leaves are labeled by elements of a free abelian group H and a certain group D(H) derived from the free Lie algebra over H. Both of these groups arise in several different topological contexts. The map eta is known to be an isomorphism over Q, bu…
Smooth family of G2-instantons over a Kummer construction.
problem Constructing a smooth family of G2-instantons over a Kummer construction.
method Extending gluing construction for G2-instantons to Kummer constructions, using a Z2-action to overcome obstructions.
result Proves the existence of a smooth 1-parameter family of G2-instantons, showing their infinitesimal rigidity and non-flatness.
We give an explicit handy (and cocycle-free) description of the groupoid of weak maps between two crossed-modules in terms of certain digrams of groups which we we call a {\em butterflies}. We define composition of butterflies and this way find a bicategory that is naturally biequivalent to the 2-category of pointed ho…
Suppose M is a compact manifold with boundary. Let N be a normal covering of M. Suppose (A,T) is an elliptic differential boundary value problem on M with lift (\tilde A,\tilde T) to N. Then the von Neumann dimension of kernel and cokernel of this lift are defined. The main result of this paper is: these numbers are fi…
The equivalence of principal bundles with transitive Lie groupoids due to Ehresmann is a well known result. A remarkable generalisation of this equivalence, due to Mackenzie, is the equivalence of principal bundle extensions with those transitive Lie groupoids over the total space of a principal bundle, which also admi…
The paper sets new bounds on metrics with positive scalar curvature.
problem Classifying metrics with positive scalar curvature.
method Lower bounds on the rank of the group of psc metrics over M.
result Lower bounds on the rank of psc metrics up to bordism.
We consider planar vector field without zeroes X and study the image of the associated Lie derivative operator LX acting on the space of smooth functions. We show that the cokernel of LX is infinite-dimensional as soon as X is not topologically conjugate to a constant vector field and that, if the topology of the integ…
The article provides conditions for unobstructedness of ASD manifolds.
problem Understanding the local structure of moduli spaces of ASD conformal structures.
method Conformally invariant conditions for ASD manifolds of positive Yamabe type.
result ASD manifolds of positive Yamabe type are unobstructed.
Let p be an odd regular prime, and assume that the Lichtenbaum-Quillen conjecture holds for K(Z[1/p]) at p. Then the p-primary homotopy type of the smooth Whitehead spectrum Wh(*) is described. A suspended copy of the cokernel-of-J spectrum splits off, and the torsion homotopy of the remainder equals the torsion homoto…
In this paper, we survey recent works on the structure of the mapping class groups of surfaces mainly from the point of view of topology. We then discuss several possible directions for future research. These include the relation between the structure of the mapping class group and invariants of 3-manifolds, the unstab…
Cohomology of Lie 2-groupsmath.AT
In this paper we study the cohomology of (strict) Lie 2-groups. We obtain an explicit Bott-Shulman type map in the case of a Lie 2-group corresponding to the crossed module . The cohomology of the Lie 2-groups corresponding to the universal crossed modules $G\to \Aut(G)$ and $G\to \Aut^+(G)$ is the abutment of …
We introduce filtered cohomologies of differential forms on symplectic manifolds. They generalize and include the cohomologies discussed in Paper I and II as a subset. The filtered cohomologies are finite-dimensional and can be associated with differential elliptic complexes. Algebraically, we show that the filtered co…
A topological approach to stratification learning is developed for point cloud data drawn from a stratified space. Given such data, our objective is to infer which points belong to the same strata. First we define a multi-scale notion of a stratified space, giving a stratification for each radius level. We then use met…
Higher hairy graph homologymath.AT
We study the hairy graph homology of a cyclic operad; in particular we show how to assemble corresponding hairy graph cohomology classes to form cocycles for ordinary graph homology, as defined by Kontsevich. We identify the part of hairy graph homology coming from graphs with cyclic fundamental group as the dihedral h…
Study rational homology cobordisms of 3-spheres and lens spaces.
problem When rational homology 3-spheres are cobordant to connected sums of lens spaces.
method Knot Floer homology combined with rational homology cobordism theory.
result Every rational homology cobordism class in the subgroup generated by lens spaces is uniquely represented by a connected sum of lens spaces.
Computes Picard groups of complex parallelizable manifolds.
problem Calculating Picard groups of specific compact complex manifolds.
method Analyzes tangent bundle triviality and uses lattice and Lie group properties.
result Computes Picard groups for certain compact complex parallelizable manifolds.
Study two homomorphisms to rational homology sphere group, proving new results on knot concordance.
problem Understanding knot concordance and homology sphere groups.
method Analyzing homomorphisms and using Tristram-Levine signatures.
result Knot concordant to a knot with determinant 1 if and only if it is smoothly slice.
The smooth rational homology cobordism group of rational homology three spheres, T, contains subgroups T_p generated by 3-manifolds with first homology p-torsion, where p is a prime. Rochlin's theorem and gauge theoretic methods show that the inclusion of the direct sum of the T_p into T has infinitely generated kernel…
We establish a long exact sequence for Legendrian submanifolds L in P x R, where P is an exact symplectic manifold, which admit a Hamiltonian isotopy that displaces the projection of L off of itself. In this sequence, the singular homology H_* maps to linearized contact cohomology CH^* which maps to linearized contact …
Study conically singular instantons over SU(3)-manifolds, proving existence and dimension formulas.
problem Existence and dimension of moduli spaces of conically singular instantons.
method Develop Fredholm deformation theory, investigate cokernel of instanton operator.
result Formula for virtual dimension of moduli space of conically singular instantons with structure group P(U(n)).
The paper shows how certain circle families in relate to sphere families in and induces nontrivial barbell diffeomorphisms.
problem Understanding the relationship between circle and sphere families in specific 3-manifolds.
method Analyzing the fundamental groups and ambient extensions of circle and sphere families.
result Induces nontrivial barbell diffeomorphisms of .
We investigate classification results for general quadratic functions on torsion abelian groups. Unlike the previously studied situations, general quadratic functions are allowed to be inhomogeneous or degenerate. We study the discriminant construction which assigns, to an integral lattice with a distinguished characte…
New Morse theory techniques glue nontransverse flowlines.
problem Gluing nontransverse gradient flowlines in Morse theory.
method Adapted OBG techniques from Hutchings and Taubes to Morse theory.
result Explicit criteria for gluing certain flowlines.
Maps between classifying spaces for certain groups are studied, with rational cohomology results.
problem Analyzing maps between classifying spaces for specific groups.
method Study of maps between null-components of homomorphism and based map spaces.
result Surjectivity of map in rational cohomology for certain groups, and non-surjectivity for others.
Uniform elliptic theory for Dirac operators on orbifold resolutions.
problem Analyzing Dirac operators on orbifold resolutions.
method Viewing orbifolds as conically fibred singular spaces and resolving them by gluing asymptotically conical fibrations.
result Uniform index formula for Dirac operators on orbifold resolutions.
Study -brane Galilean and Carrollian geometries via intrinsic torsion.
problem Characterize -brane Galilean and Carrollian geometries via intrinsic torsion.
method Analyze intrinsic torsions as representations of , interpret geometrically, and use physics-inspired methods.
result Recover classification of -brane Galilean geometries and relate to ()-brane Carrollian geometries.
This article gives a study of the higher-dimensional Penrose transform between conformally invariant massless fields on space-time and cohomology classes on twistor space, where twistor space is defined to be the space of projective pure spinors of the conformal group. We focus on the 6-dimensional case in which twisto…