Related papers: Tangent structures for divided power algebras
Following the pattern from linear logic, the coKleisli category of a differential category is a Cartesian differential category. What then is the coEilenberg-Moore category of a differential category? The answer is a tangent category! A key…
Three definitions of a differential form on a tangent structure are considere. It is proved that the (covariant) definition given by Souriau (as a collection of forms indexed by the plaques) is equivalent to a smooth section of the…
We show that a diffeological bundle gives rise to an exact sequence of internal tangent spaces. We then introduce two new classes of diffeological spaces, which we call weakly filtered and filtered diffeological spaces, whose tangent spaces…
We provide a differential structure on arbitrary cleft extensions $B:=A^{\mathrm{co}H}\subseteq A$ for an $H$-comodule algebra $A$. This is achieved by constructing a covariant calculus on the corresponding crossed product algebra…
For a pre-Lie-Yamaguti algebra $A$, by using its sub-adjacent Lie-Yamaguti algebra $A^c$, we are able to construct a semidirect product Lie-Yamaguti algebra via a representation of $A^c$. The investigation of such semidirect Lie-Yamaguti…
For a compact complex manifold, we introduce holomorphic foliations associated with certain abelian subgroups of the automorphism group. Such foliations are generalizations of holomorphic principal torus bundles. If there exists a…
We study the local differential geometry of varieties $X^n\subset \Bbb C\Bbb P^{n+a}$ with degenerate secant and tangential varieties. We show that the second fundamental form of a smooth variety with degenerate tangential variety is…
We equip the direct limit of tangent bundles of paracompact finite dimensional manifolds with a structure of convenient vector bundle with structural group $GL(\infty,\mathbb{R}) =\underrightarrow{\lim}GL(\mathbb{R}^{n})$.
Inspired by bordered Floer homology, we describe a type A structure on a Khovanov homology for a tangle, which complements the type D structure in a previous paper. The type A structure is a differential module over a certain algebra. This…
This paper studies the homotopy theory of parameterized spectrum objects in a model category from a global point of view. More precisely, for a model category $\mathcal{M}$ satisfying suitable conditions, we construct a relative model…
A tangent category is a categorical abstraction of the tangent bundle construction for smooth manifolds. In that context, Cockett and Cruttwell develop the notion of differential bundle which, by work of MacAdam, generalizes the notion of…
Consider the smooth sections of the tangent bundle of a reductive homogeneous space. This is a vector space over the field of real numbers. The canonical connection acts as a linear binary operator on this vector space, making it an…
We study generalized Kaehler manifolds for which the corresponding complex structures commute and classify completely the compact generalized Kaehler four-manifolds for which the induced complex structures yield opposite orientations.
We study quotients of multi-graded bundles, including double vector bundles. Among other things, we show that any such quotient fits into a tower of affine bundles. Applications of the theory include a construction of normal bundles for…
We define self-distributive structures in the categories of coalgebras and cocommutative coalgebras. We obtain examples from vector spaces whose bases are the elements of finite quandles, the direct sum of a Lie algebra with its ground…
We will show that gauge theory can be described by an almost product structure, which is a certain type of endomorphism of the tangent bundle. We will recover the gauge field strength as the Nijenhuis tensor of this endomorphism. We discuss…
We introduce a derived enhancement of the moduli space of sections defined by Chang-Li, and we compute its tangent complex. Special cases of this moduli space include stable maps and stable quasi-maps. As an application, we prove that…
We obtain the natural diagonal almost product and locally product structures on the total space of the cotangent bundle of a Riemannian manifold. We find the Riemannian almost product (locally product) and the (almost) para-Hermitian…
Let $S$ be a Noetherian scheme, and let $X$ be a scheme over $S$, such that all relative symmetric powers of $X$ over $S$ exist. Assume that either $S$ is of pure characteristic $0$ or $X$ is flat over $S$. Assume also that the structural…
A new class of noncommutative $k$-algebras (for $k$ an algebraically closed field) is defined and shown to contain some important examples of quantum groups. To each such algebra, a first order theory is assigned describing models of a…