Remarks on the Schouten-Nijenhuis bracket
Knit products of graded Lie algebras and groups
Let and be graded Lie algebras whose grading is in or , but only one of them. Suppose that is a derivatively knitted pair of representations for , i.e. and satisfy equations which look “derivatively knitted"; then , endowed with a suitable bracket, which mimics semidirect products on both sides, becomes a graded Lie algebra . This graded Lie algebra is called the knit product of and . The author investigates the general situation for any graded Lie subalgebras and of a graded...
The cohomology of the diffeomorphism group of a manifold is a Gelfand-Fuks cohomology
Description of infinite-dimensional abelian regular Lie groups.
All natural concomitants of vector valued differential forms
A note on n-ary Poisson brackets
An -ary Poisson bracket (or generalized Poisson bracket) on the manifold is a skew-symmetric -linear bracket of functions which is a derivation in each argument and satisfies the generalized Jacobi identity of order , i.e., being the symmetric group. The notion of generalized Poisson bracket was introduced by et al. in [J. Phys. A, Math. Gen. 29, No. 7, L151–L157 (1996; Zbl 0912.53019) and J. Phys. A, Math. Gen. 30, No. 18, L607–L616 (1997; Zbl 0932.37056)]. They established...
The flow completion of a manifold with vector field.
Regular infinite dimensional Lie groups.
Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms.
Completing Lie algebra actions to Lie group actions.
Zum Tensorprodukt von Funktoren auf Kategorien von Banachräumen.
A convenient setting for differential geometry and global analysis
A convenient setting for differential geometry and global analysis II
On a construction connecting Lie algebras with general algebras
Tensor fields and connections on holomorphic orbit spaces of finite groups.
Extensions of super Lie algebras.
Lifting smooth curves over invariants for representations of compact Lie groups. II.
The homotopy type of the space of degree 0 immersed plane curves.
The space B = Imm (S, R) / Diff (S) of all immersions of rotation degree 0 in the plane modulo reparameterizations has homotopy groups π(B ) = Z, π(B ) = Z, and π(B ) = 0 for k ≥ 3.
Riemannian geometries on spaces of plane curves
We study some Riemannian metrics on the space of smooth regular curves in the plane, viewed as the orbit space of maps from to the plane modulo the group of diffeomorphisms of , acting as reparametrizations. In particular we investigate the metric, for a constant , where is the curvature of the curve and , are normal vector fields to . The term is a sort of geometric Tikhonov regularization because, for , the geodesic distance between any two distinct curves is 0, while for the...
Natural transformations in differential geometry
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