arXiv research

In this notes it will be provided a set of techniques which can help one to understand the proof of the Hochschild-Kostant-Rosenberg theorem for differentiable manifolds. Precise definitions of multidiferential operators and polyderivations on an algebra are given, allowing to work on these concepts, when the algebra i…

Global homotopies upgrade classical map in differential geometry.

The central result here is an explicit computation of the Hochschild and cyclic homologies of a natural smooth subalgebra of stable continuous trace algebras having smooth manifolds X as their spectrum. More precisely, the Hochschild homology is identified with the space of differential forms on X, and the periodic cyc…

The paper compares two notions of invariance in Hochschild cohomology spaces.

Proves formality conjecture for Hamiltonian actions using equivariant Hochschild-Kostant-Rosenberg quasi-isomorphism.

$\newcommand{\poly}{_{\operatorname{poly}}^{\bullet}}\newcommand{\td}{(\operatorname{td}_{L/A}^{\nabla})^{\frac{1}{2}}}\newcommand{\cx}[1]{\operatorname{tot}\big(Γ(Λ^\bullet A^\vee)\otimes_R\mathcal{#1}\poly\big)}\newcommand{\cy}[1]{\mathbb{H}^\bullet_{\operatorname{CE}}(A,\mathcal{#1}\poly)}$Kontsevich's formality the…

To any $\mathfrak{g}$-manifold $M$ are associated two dglas $\operatorname{tot}\big(Λ^{\bullet} \mathfrak{g}^\vee \otimes_{\Bbbk} T_{\operatorname{poly}}^{\bullet} \big)$ and $\operatorname{tot} \big(Λ^{\bullet} \mathfrak{g}^\vee\otimes_{\Bbbk} D_{\operatorname{poly}}^{\bullet} \big)$, whose cohomologies $H_{\operatorn…

Study cohomology of Lie algebroids over algebraic spaces using derived functors and Čech cohomology.

Researchers compute Hochschild cohomology of Grassmannians.

AI generates theorems and proofs for training theorem provers.

Global inverse function theorem proved easily using Riemannian geometry.

A new comparison theorem for geometric spaces.

The paper proves a new theorem in Riemannian geometry and offers a new proof for Toponogov's theorem in Alexandrov geometry.

Paper develops formulas and theorems in Hermitian geometry.

The paper proves three circles theorems and Liouville type theorems for subharmonic and holomorphic functions.

Revises a theorem by Thurston, finding a counter-example and a weaker version.

Proofs for Moon's theorem and its generalization.

Proves Markov theorem for trivalent braids using L-move approach.

New theorem for doodles on sphere, similar to Markov's.

Analyzes Saito vanishing theorem using $L^{2}$ methods.

Investigates proving geometric theorems over complex and real numbers using tilings.

Extends calculus theorem to higher dimensions.

Extends symplectic reduction and theorem to Lie algebroids.

Paper generalizes complex Brunn-Minkowski theory and proves new extension theorems.

Proves Thurston's bounded image theorem for Haken manifolds.

Method upgrades limit theorems to mixing limit theorems for dynamical systems.

Formulates Index III lemma and Rauch III theorem with applications.

In LM, we proved a family version of the famous Witten rigidity theorems and several family vanishing theorems for elliptic genera. In this paper, we gerenalize our theorems LM in two directions. First we establish a family rigidity theorem for the Dirac operator on loop space twisted by general positive energy loop gr…

The paper explains the topological origin of the distinction between incidence theorems over division rings and fields.

INT benchmark tests theorem proving agents' ability to generalize to unseen theorems.

Proves two theorems on odd-dimensional manifolds with boundary.

Sharp convergence theorem for sphere submanifolds proved.

Abstracts a theorem for non-smooth maps in infinite dimensions.

A homological selection theorem for C-spaces, as well as, a finite-dimensional homological selection theorem is established. We apply the finite-dimensional homological selection theorem to obtain fixed-point theorems for usco homologically UV^n set-valued maps.

Atiyah-Singer theorem links math fields, predicts topological insights.

Paper generalizes a theorem for real analytic singularities.

The paper proves injectivity and vanishing theorems on compact Kahler manifolds.

The paper proves sphere theorems for submanifolds in Kähler manifolds.

Several proofs of Fáry--Milnor theorem are presented.

Reviews g-theorem and hard Lefschetz theorem for face rings.

Reidemeister's theorem proved using smooth functions and transversality.

Proves an analytic Bertini theorem, generalizing previous work.

Sphere theorems for submanifolds in Kähler and Sasaki spaces.

This note explores comparison geometry concepts and theorems.

Proof of Tait-Kneser theorem and related variations using Lorentzian geometry.

Proves Skoda's Division Theorem using degeneration and positivity of direct image bundles.

We show how Latour's theorem can be understood as a natural generalization of the $s$-cobordism theorem for cohomology classes $u\in H^1(M;\mathbb{R})$. The $s$-cobordism theorem becomes a special degenerate case when $u=0$.

Generalizes symplectic reduction to cosymplectic groupoid actions.