arXiv research

In this work we prove a residue formula for Morita-Futaki-Bott invariant with respect any holomorphic vector fields with isolated (possibly degenerated) singularities in terms of Grothendieck's residues.

Researchers determine Baum-Bott residues for foliations without generic hypothesis.

New potential functions reveal Frobenius-like structure in weighted hyperplane arrangements.

Constructs currents representing Baum-Bott residues for foliations.

The study explores how different Grothendieck topologies and functors between categories preserve locality.

Every symmetric polytope is a norm in the Grothendieck group of R^n polytopes.

3-manifold groups are rigid under certain conditions.

Shows natural quasi-Poisson structure on multiplicative Grothendieck-Springer space.

Proves Grothendieck-Teichmüller group acts on specific mapping class groups.

Study of forms on inertia spaces using Grauert--Grothendieck complex.

Proves a theorem for complex flat vector bundles using differential forms.

Grothendieck proposes a new topology for semialgebraic and semianalytic geometry.

We give a direct proof that the Freed-Lott differential analytic index is well defined and a condensed proof of the differential Grothendieck-Riemann-Roch theorem. As a byproduct we also obtain a direct proof that the R/Z analytic index is well defined and a condensed proof of the R/Z Grothendieck-Riemann-Roch theorem.

Develops equivariant Chern characters for coherent sheaves with group actions.

Study on string links invariant under associator choice and Grothendieck--Teichmüller group action.

3-manifold groups are uniquely identifiable via their profinite completions.

We identify the Grothendieck group of the tangle Floer dg algebra with a tensor product of certain $U_q(gl(1|1))$ representations. Under this identification, up to a scalar factor, the map on the Grothendieck group induced by the tangle Floer dg bimodule associated to a tangle agrees with the Reshetikhin-Turaev homomor…

Grothendieck reformulated Teichmüller's construction using category theory.

Study automorphism groups of braid groups with 4 or more strings.

The aim of this note is to take benefit of the foam nature of the Khovanov-Kuperberg algebras to compute the Grothendieck groups of their categories of finitely generated projective modules. The computation relies on the Hattori-Stallings trace and some geometrical properties of foams in a solid torus.

Study of orbifold Chern character using superconnections.

In this paper we give a simplified proof of the flat Grothendieck-Riemann-Roch theorem. The proof makes use of the local family index theorem and basic computations of the Chern-Simons form. In particular, it does not involve any adiabatic limit computation of the reduced eta-invariant.

Explains historical connections between vector bundle splitting and Riemann-Hilbert problems.

This paper attempts to relate some ideas of Grothendieck in his Esquisse d'un programme and some of the recent results on 2-dimensional topology and geometry. Especially, we shall discuss the Teichmüller theory, the mapping class groups, $SL(2, \bold C)$ representation variety of surface groups, and Thurston's theory o…

Paper constructs Chern character for coherent sheaves.

Proves a complex flat vector bundle theorem using index theory.

Researchers prove Lie algebras of differential operators and Grothendieck constructions coincide.

The paper studies the commutator subgroups of twin groups and their properties.

The paper proves stabilization in hypersurface sections using Grothendieck rings and probabilistic methods.

Desingularizes singular spaces using sheaves and groupoids.

We identify a free-abelian group from integral polytopes and its properties.

Computes second homology groups of orbifold groups, proving profinite rigidity and Grothendieck pairs.

Integrally splits L-spectra of integers into simpler components.

The study explores rigidity in groups and their products, finding uncountable families of non-isomorphic subgroups.

Study of Fukaya category on surfaces with mapping class group action.

Calculates characteristic classes of flat vector bundles on complex fibers.

In this paper we study the problem of approximation of the $L^2$-topological invariants by their finite dimensional analogues. We obtain generalizations of the theorem of Lück, dealing with towers of finitely sheeted normal coverings. We prove approximation theorems, establishing relations between the homological invar…

In the present paper we discuss an independent on the Grothendieck-Sato isomorphism approach to the Riemann-Roch-Hirzebruch formula for an arbitrary differential operator. Instead of the Grothendieck-Sato isomorphism, we use the Topological Quantum Mechanics (more or less equivalent to the well-known constructions with…

We prove that the Grothendieck-Springer simultaneous resolution viewed as a correspondence between the adjoint quotient of a Lie algebra and its maximal torus is Lagrangian in the sense of shifted symplectic structures. As Hamiltonian spaces can be interpreted as Lagrangians in the adjoint quotient, this allows one to …

Geometric models for representations up to homotopy using simplicial vector bundles.

The paper shows plentiful non-homotopy finite Poincaré duality spaces.

Continuity shown for Yang-Mills flow on semistable bundles.

Study representation rings and dimension functions for fusion systems.

In this paper we give a proof of an index theorem by Bismut. As a consequence we obtain another proof of the Grothendieck-Riemann-Roch theorem in differential cohomology.

SDP achieves exponential error rate in cluster estimation for Stochastic Block Model.

We construct the Fukaya category of a closed surface equipped with an area form using only elementary (essentially combinatorial) methods. We also compute the Grothendieck group of its derived category.

This note announces a general construction of characteristic currents for singular connections on a vector bundle. It develops, in particular, a Chern-Weil-Simons theory for smooth bundle maps $α: E \rightarrow F$ which, for smooth connections on $E$ and $F$, establishes formulas of the type $$ φ\ = \ \text{\rm Res}_φΣ…

In this thesis, we study deformations of compact holomorphic Poisson manifolds and algebraic Poisson schemes in the framework of Kodaira-Spencer's analytic deformation theory and Grothendieck's algebraic deformation theory.