Related papers: Variations of rational higher tangential structure…
In this note we provide a new perspective on the topological parts of several action functionals in string and M-theory. We show that rationally these can be viewed as large gauge transformations corresponding to variations of higher…
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 constructed abstractly starting from an arbitrary almost Lie…
We analyze the geometrical background under which many Lie groups relevant to particle physics are endowed with a (possibly multiple) hexagonal structure. There are several groups appearing, either as special holonomy groups on the…
String structures in degree four are associated with cancellation of anomalies of string theory in ten dimensions. Fivebrane structures in degree eight have recently been shown to be associated with cancellation of anomalies associated to…
We develop a description of higher gauge theory with higher groupoids as gauge structure from first principles. This approach captures ordinary gauge theories and gauged sigma models as well as their categorifications on a very general…
We give a review of truncated L$_\infty$ algebras, as used in the study of higher gauge theory. These structures are believed to hold the correct properties to adequately describe gauge theory of extended objects. We discuss how to…
A gauge theory is associated with a principal bundle endowed with a connection permitting to define horizontal lifts of paths. The horizontal lifts of surfaces cannot be defined into a principal bundle structure. An higher gauge theory is…
We review some definitions and basic notions relating to generalised spin structures and introduce the notion of reducibility. We discuss connections on these structures, define a covariant Lie derivative for associated bundles and develop…
We propose a definition of a "higher" version of the omni-Lie algebroid and study its isotropic and involutive subbundles. Our higher omni-Lie algebroid is to (multi)contact and related geometries what the higher generalized tangent bundle…
Higher structures - infinity algebras and other objects up to homotopy, categorified algebras, `oidified' concepts, operads, higher categories, higher Lie theory, higher gauge theory... - are currently intensively investigated in…
In this paper, we describe a geometric setting for higher-order lagrangian problems on Lie groups. Using left-trivialization of the higher-order tangent bundle of a Lie group and an adaptation of the classical Skinner-Rusk formalism, we…
The notion of global higher-form symmetries has received much attention, but leaves room for a more systematic mathematical formulation. In this article, we highlight the concept of higher automorphism bundles from the field of higher…
String structures have played an important role in algebraic topology, via elliptic genera and elliptic cohomology, in differential geometry, via the study of higher geometric structures, and in physics, via partition functions. We extend…
We survey interactions between the topology and the combinatorics of complex hyperplane arrangements. Without claiming to be exhaustive, we examine in this setting combinatorial aspects of fundamental groups, associated graded Lie algebras,…
Configurations of fivebranes, twobranes and fourbranes in type IIA string theory, which give (1+1) dimensional supersymmetric gauge theories in the low energy limit, are constructed. It is shown that these brane configurations are…
These are notes for four lectures on higher structures in M-theory as presented at workshops at the Erwin Schroedinger Institute and Tohoku University. The first lecture gives an overview of systems of multiple M5-branes and introduces the…
Given a vector bundle $A\to M$ we study the geometry of the graded manifolds $T^*[k]A[1]$, including their canonical symplectic structures, compatible Q-structures and Lagrangian Q-submanifolds. We relate these graded objects to classical…
We consider the topological and geometric structures associated with cohomological and homological objects in M-theory. For the latter, we have M2-branes and M5-branes, the analysis of which requires the underlying spacetime to admit a…
Studying the M-branes leads us naturally to new structures that we call Membrane-, Membrane^c-, String^K(Z,3)- and Fivebrane^K(Z,4)-structures, which we show can also have twisted counterparts. We study some of their basic properties,…
The notion of a \emph{higher-order algebroid}, as introduced by J\'o\'zwikowski and Rotkiewicz in their work \emph{Higher-order analogs of Lie algebroids via vector bundle comorphisms} (SIGMA, 2018), generalizes the concepts of a…