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pro vyhledávání: '"53c05"'
We develop the notions of connections and curvature for general Lie-Rinehart algebras without using smoothness assumptions on the base space. We present situations when a connection exists. E.g., this is the case when the underlying module is finitel
Externí odkaz:
http://arxiv.org/abs/2411.04829
Autor:
Kristel, Peter, Schmeding, Alexander
The Stacey-Roberts Lemma states that the pushforward of a surjective submersion between finite-dimensional manifolds gives rise to a submersion on infinite-dimensional manifolds of smooth mappings by pushforward. This result is foundational for many
Externí odkaz:
http://arxiv.org/abs/2411.00587
We construct global homotopies to compute differential Hochschild cohomologies in differential geometry. This relies on two different techniques: a symbol calculus from differential geometry and a coalgebraic version of the van Est theorem. Not only
Externí odkaz:
http://arxiv.org/abs/2410.15903
Autor:
Stava, Jonatan
Lie Yamaguti algebras appear naturally on the smooth sections of the tangent bundle of a reductive homogeneous space when we interpret the torsion and curvature as algebraic operators. In this article we present a description of the free Lie Yamaguti
Externí odkaz:
http://arxiv.org/abs/2408.10815
Autor:
Jotz, M., Marchesini, R.
Twisted Lie algebroid cohomologies, i.e. with values in representations, are shown to be Lie algebroid homotopy-invariant. Several important classes of examples are discussed. As an application, a generalized version of the Poincar\'e lemma is given
Externí odkaz:
http://arxiv.org/abs/2407.19750
Autor:
Fernandez, Javier, Kordon, Francisco
In this paper we introduce the Integration Problem for principal connections. Just as a principal connection on a principal bundle $\phi:Q\rightarrow M$ may be used to split $TQ$ into horizontal and vertical subbundles, a discrete connection may be u
Externí odkaz:
http://arxiv.org/abs/2407.13614
The inverse of the metric matrices on the Siegel-Jacobi upper half space ${\mathcal{X}}^J_n$, invariant to the restricted real Jacobi group $G^J_n(\mathbb{R})_0$ and extended Siegel-Jacobi $\tilde{{\mathcal{X}}}^J_n$ upper half space, invariant to th
Externí odkaz:
http://arxiv.org/abs/2407.04310
There is an abstract notion of connection in any tangent category. In this paper, we show that when applied to the tangent category of affine schemes, this recreates the classical notion of a connection on a module (and similarly, in the tangent cate
Externí odkaz:
http://arxiv.org/abs/2406.15137
We present a complete classification of simply-connected pluriclosed manifolds with parallel Bismut torsion, extending previously known results in the literature. Consequently, we also establish a splitting theorem for compact manifolds that are both
Externí odkaz:
http://arxiv.org/abs/2406.07039
Autor:
Chakraborty, Sujoy, Paul, Arjun
Let $X$ be a smooth complex projective variety equipped with an action of a linear algebraic group $G$ over $\mathbb{C}$. Let $D$ be a reduced effective divisor on $X$ that is invariant under the $G$--action on $X$. Let $s_D$ be the canonical section
Externí odkaz:
http://arxiv.org/abs/2405.20699