Quotients of double vector bundles and multigraded bundles

TL;DR

This paper investigates quotients of multi-graded bundles, especially double vector bundles, demonstrating they form a tower of affine bundles and applying this to construct normal bundles for weighted submanifolds and intersecting submanifolds.

Contribution

It introduces a framework showing quotients of multi-graded bundles can be structured as towers of affine bundles, with applications to normal bundle constructions.

Findings

Quotients of multi-graded bundles form towers of affine bundles.

Application to constructing normal bundles for weighted submanifolds.

Application to normal bundles for pairs of submanifolds with clean intersection.

Abstract

We study quotients of multi-graded bundles, including double vector bundles. Among other things, we show that any such quotient fits into a tower of affine bundles. Applications of the theory include a construction of normal bundles for weighted submanifolds, as well as for pairs of submanifolds with clean intersection.