Quotients of double vector bundles and multigraded bundles

Eckhard Meinrenken

doi:10.3934/jgm.2021027

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2022, Volume 14, Issue 2: 307-329. Doi: 10.3934/jgm.2021027

This issue Previous Article Poisson double structures Next Article

Quotients of double vector bundles and multigraded bundles

Eckhard Meinrenken^,

Mathematics Department, University of Toronto, 40 St George Street, Toronto, ON M5S 2E4, Canada

^* Corresponding author: Eckhard Meinrenken
^* Corresponding author: Eckhard Meinrenken

Received: November 30, 2020

Published: June 2022

The author is supported by NSERC Discovery Grant 480547

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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.

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Mathematics Subject Classification: Primary: 53C05, 53D17; Secondary: 55R65.

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