Homology Tangent Bundles and Universal Bundles1

Some aspects of cosheaves on diffeological spaces

We define a notion of cosheaves on diffeological spaces by cosheaves on the site of plots. This provides a framework to describe diffeological objects such as internal tangent bundles, the Poincar'{e} groupoids, and furthermore, homology theories such as cubic homology in diffeology by the language of cosheaves. We show that every cosheaf on a diffeological space induces a cosheaf in terms of t...

A Characterization of the Infinitesimal Conformal Transformations on Tangent Bundles

On Infinitesimal Conformal Transformations of the Tangent Bundles with the Generalized Metric

Let  be an n-dimensional Riemannian manifold, and  be its tangent bundle with the lift metric. Then every infinitesimal fiber-preserving conformal transformation  induces an infinitesimal homothetic transformation on .  Furthermore,  the correspondence   gives a homomorphism of the Lie algebra of infinitesimal fiber-preserving conformal transformations on  onto the Lie algebra of infinitesimal ...

Para-Kahler tangent bundles of constant para-holomorphic sectional curvature

We characterize the natural diagonal almost product (locally product) structures on the tangent bundle of a Riemannian manifold. We obtain the conditions under which the tangent bundle endowed with the determined structure and with a metric of natural diagonal lift type is a Riemannian almost product (locally product) manifold, or an (almost) para-Hermitian manifold. We find the natural diagona...

On Kontsevich’s Characteristic Classes for Higher Dimensional Homology Sphere Bundles and Milnor’s 0-invariant

This paper is concerned with M. Kontsevich’s universal characteristic classes of smooth bundles with fiber a ‘singularly’ framed odd-dimensional homology sphere. The main object of the present paper is to show that Kontsevich classes for fiber dimensions greater than 3 are highly non-trivial even after being made framing independent. We have two approaches: (i) explicit framing correction with ...