2,424 research outputs found
Operads within monoidal pseudo algebras
A general notion of operad is given, which includes as instances, the operads
originally conceived to study loop spaces, as well as the higher operads that
arise in the globular approach to higher dimensional algebra. In the framework
of this paper, one can also describe symmetric and braided analogues of higher
operads, likely to be important to the study of weakly symmetric, higher
dimensional monoidal structures
The two definitions of the index difference
Given two metrics of positive scalar curvature metrics on a closed spin
manifold, there is a secondary index invariant in real -theory. There exist
two definitions of this invariant, one of homotopical flavour, the other one
defined by a index problem of Atiyah-Patodi-Singer type. We give a complete and
detailed proof of the folklore result that both constructions yield the same
answer. Moreover, we generalize this to the case of two families of positive
scalar curvature metrics, parametrized by a compact space. In essence, we prove
a generalization of the classical "spectral-flow-index theorem" to the case of
families of real operators.Comment: Revised versio
About the classification of the holonomy algebras of Lorentzian manifolds
The classification of the holonomy algebras of Lorentzian manifolds can be
reduced to the classification of irreducible subalgebras
that are spanned by the images of linear
maps from to satisfying an identity similar to
the Bianchi one. T. Leistner found all such subalgebras and it turned out that
the obtained list coincides with the list of irreducible holonomy algebras of
Riemannian manifolds. The natural problem is to give a simple direct proof to
this fact. We give such proof for the case of semisimple not simple Lie
algebras .Comment: 9 pages, the final versio
- β¦