132 citations · 232 across the 10 of their papers we have counts for
12 papers
Equivalence functors in graded supergeometry
Katarzyna Grabowska, Janusz Grabowski, Mikołaj Rotkiewicz
It has recently been proved that the category of N-manifolds of degree , that is, -graded supermanifolds of degree for which the parity agrees with the gradation,…
Exploring the Structure of Higher Algebroids
Mikołaj Rotkiewicz
The notion of a \emph{higher-order algebroid}, as introduced by Jóźwikowski and Rotkiewicz in their work \emph{Higher-order analogs of Lie algebroids via vector bundle comorphisms}…
Graded covering of a supermanifold I. The case of a Lie supergroup
Mikolaj Rotkiewicz, Elizaveta Vishnyakova
We generalize the Donagi and Witten construction of a first obstruction class for splitting of a supermanifold via differential operators using the theory of -fold vector bundle…
Higher-Order Analogs of Lie Algebroids via Vector Bundle Comorphisms
Michał Jóźwikowski, Mikołaj Rotkiewicz
We introduce the concept of a higher algebroid, generalizing the notions of an algebroid and a higher tangent bundle. Our ideas are based on a description of (Lie) algebroids as ve…
Duality for graded manifolds
Janusz Grabowski, Michał Jóźwikowski, Mikołaj Rotkiewicz
We study the notion of duality in the context of graded manifolds. For graded bundles, somehow like in the case of Gelfand representation and the duality: points vs. functions, we…
A note on actions of some monoids
Michal Jozwikowski, Mikolaj Rotkiewicz
Smooth actions of the multiplicative monoid of real numbers on manifolds lead to an alternative, and for some reasons simpler, definition of a vector bundle, a…
Polarisation of Graded Bundles
Andrew James Bruce, Janusz Grabowski, Mikolaj Rotkiewicz
We construct the full linearisation functor which takes a graded bundle of degree (a particular kind of graded manifold) and produces a -fold vector bundle. We fully charact…
Prototypes of higher algebroids with applications to variational calculus
Michał Jóźwikowski, Mikołaj Rotkiewicz
Reductions of higher tangent bundles of Lie groupoids provide natural examples of geometric structures which we would like to call higher algebroids. Such objects can be also const…
Bundle-theoretic methods for higher-order variational calculus
Michał Jóźwikowski, Mikołaj Rotkiewicz
We present a geometric interpretation of the integration-by-parts formula on an arbitrary vector bundle. As an application we give a new geometric formulation of higher-order varia…
Graded bundles and homogeneity structures
Janusz Grabowski, Mikolaj Rotkiewicz
We introduce the concept of a graded bundle which is a natural generalization of the concept of a vector bundle and whose standard examples are higher tangent bundles T^nQ playing…
Double Affine Bundles
Janusz Grabowski, Mikolaj Rotkiewicz, Pawel Urbanski
A theory of double affine and special double affine bundles, i.e. differential manifolds with two compatible (special) affine bundle structures, is developed as an affine counterpa…
Higher vector bundles and multi-graded symplectic manifolds
Janusz Grabowski, Mikolaj Rotkiewicz
A natural explicit condition is given ensuring that an action of the multiplicative monoid of non-negative reals on a manifold F comes from homotheties of a vector bundle structure…