Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
The Stacey-Roberts Lemma for Banach Manifolds
View through CrossRef
The Stacey-Roberts lemma states that a surjective submersion between finite-dimensional manifolds gives rise to a submersion on infinite-dimensional manifolds of smooth mappings by pushforward. This result is foundational for many constructions in infinite-dimensional differential geometry such as the construction of Lie groupoids of smooth mappings. We generalise the Stacey-Roberts lemma to Banach manifolds which admit smooth partitions of unity.The new approach also remedies an error in the original proof of the result for the purely finite-dimensional setting.
SIGMA (Symmetry, Integrability and Geometry: Methods and Application)
Title: The Stacey-Roberts Lemma for Banach Manifolds
Description:
The Stacey-Roberts lemma states that a surjective submersion between finite-dimensional manifolds gives rise to a submersion on infinite-dimensional manifolds of smooth mappings by pushforward.
This result is foundational for many constructions in infinite-dimensional differential geometry such as the construction of Lie groupoids of smooth mappings.
We generalise the Stacey-Roberts lemma to Banach manifolds which admit smooth partitions of unity.
The new approach also remedies an error in the original proof of the result for the purely finite-dimensional setting.
Related Results
Riemannian Curvature of a Sliced Contact Metric Manifold
Riemannian Curvature of a Sliced Contact Metric Manifold
Contact geometry become a more important issue in the mathematical world with the works which had done in the 19th century. Many mathematicians have made studies on contact manifol...
LVM manifolds and lck metrics
LVM manifolds and lck metrics
Abstract
In this paper, we compare two type of complex non-Kähler manifolds : LVM and lck manifolds. First, lck manifolds (for locally conformally Kähler manifolds) admit a...
PERUMUMAN LEMMA SNAKE DAN LEMMA LIMA
PERUMUMAN LEMMA SNAKE DAN LEMMA LIMA
Abstrak. Barisan -eksak merupakan perumuman dari barisan eksak yang diperkenalkan oleh Davvaz dan Parnian-Garamaleky. Dalam tulisan ini akan dikaji perumuman dari Lemma Snake dan L...
Shared Actuator Manifold - An Innovative Conception to MInimize Costs
Shared Actuator Manifold - An Innovative Conception to MInimize Costs
Abstract
Subsea Manifold has been used as a very attractive alternative in the development of subsea fields. The discover of giant fields in deep waters and the c...
Integrability on Direct Limits of Banach Manifolds
Integrability on Direct Limits of Banach Manifolds
In this paper, we study several objects in the framework of direct limits of anchored Banach bundles over particular convenient manifolds (direct limits of Banach manifolds). In pa...
The Horizontal Lemma
The Horizontal Lemma
This chapter contains the statement and proof of the Horizontal Lemma. The proof follows a similar outline as in Chapter 10. The chapter is organized as follows. Section 11.2 uses ...
Direct limits in categories of normed vector lattices and Banach lattices
Direct limits in categories of normed vector lattices and Banach lattices
AbstractAfter collecting a number of results on interval and almost interval preserving linear maps and vector lattice homomorphisms, we show that direct systems in various categor...
Remarkable lives: Khia Stacey in conversation with Robert Hurst
Remarkable lives: Khia Stacey in conversation with Robert Hurst
Purpose
The purpose of this paper is to share Khia Stacey’s story.
Design/methodology/approach
Khia Stacey wrote a short piece detailing her journey, and she was then interviewed...