Diffeomorphisms and Embeddings of Manifolds

Sungbok Hong; John Kalliongis; Darryl McCullough; J. Hyam Rubinstein

doi:10.1007/978-3-642-31564-0_2

Diffeomorphisms and Embeddings of Manifolds

Sungbok Hong, John Kalliongis, Darryl McCullough, J. Hyam Rubinstein

Research output: Chapter in Book/Report/Conference proceeding › Chapter

11 Citations (Scopus)

Abstract

This chapter contains foundational material on spaces of diffeomorphisms and embeddings. Such spaces are known to be Fréchet manifolds, separable when the manifolds involved are compact. Versions of these and related facts are developed for manifolds with boundary, as well as in the context of fiber-preserving diffeomorphisms and maps. The latter utilizes a modification of the exponential map, called the aligned exponential, adapted to the fibered structure.

Original language	English
Title of host publication	Diffeomorphisms of Elliptic 3-Manifolds
Publisher	Springer Verlag
Pages	9-17
Number of pages	9
ISBN (Print)	9783642315633
DOIs	https://doi.org/10.1007/978-3-642-31564-0_2
Publication status	Published - 2012

Publication series

Name	Lecture Notes in Mathematics
Volume	2055
ISSN (Print)	0075-8434
ISSN (Electronic)	1617-9692

Bibliographical note

Publisher Copyright:
© 2012, Springer-Verlag Berlin Heidelberg.

Keywords

Homotopy Type
Horizontal Lift
Horizontal Part
Local Chart
Vector Field

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1007/978-3-642-31564-0_2

Cite this

@inbook{cb9fd4f9fae9444baff9fcd290e5d9aa,

title = "Diffeomorphisms and Embeddings of Manifolds",

abstract = "This chapter contains foundational material on spaces of diffeomorphisms and embeddings. Such spaces are known to be Fr{\'e}chet manifolds, separable when the manifolds involved are compact. Versions of these and related facts are developed for manifolds with boundary, as well as in the context of fiber-preserving diffeomorphisms and maps. The latter utilizes a modification of the exponential map, called the aligned exponential, adapted to the fibered structure.",

keywords = "Homotopy Type, Horizontal Lift, Horizontal Part, Local Chart, Vector Field",

author = "Sungbok Hong and John Kalliongis and Darryl McCullough and Rubinstein, \{J. Hyam\}",

note = "Publisher Copyright: {\textcopyright} 2012, Springer-Verlag Berlin Heidelberg.",

year = "2012",

doi = "10.1007/978-3-642-31564-0\_2",

language = "English",

isbn = "9783642315633",

series = "Lecture Notes in Mathematics",

publisher = "Springer Verlag",

pages = "9--17",

booktitle = "Diffeomorphisms of Elliptic 3-Manifolds",

}

TY - CHAP

T1 - Diffeomorphisms and Embeddings of Manifolds

AU - Hong, Sungbok

AU - Kalliongis, John

AU - McCullough, Darryl

AU - Rubinstein, J. Hyam

PY - 2012

Y1 - 2012

N2 - This chapter contains foundational material on spaces of diffeomorphisms and embeddings. Such spaces are known to be Fréchet manifolds, separable when the manifolds involved are compact. Versions of these and related facts are developed for manifolds with boundary, as well as in the context of fiber-preserving diffeomorphisms and maps. The latter utilizes a modification of the exponential map, called the aligned exponential, adapted to the fibered structure.

AB - This chapter contains foundational material on spaces of diffeomorphisms and embeddings. Such spaces are known to be Fréchet manifolds, separable when the manifolds involved are compact. Versions of these and related facts are developed for manifolds with boundary, as well as in the context of fiber-preserving diffeomorphisms and maps. The latter utilizes a modification of the exponential map, called the aligned exponential, adapted to the fibered structure.

KW - Homotopy Type

KW - Horizontal Lift

KW - Horizontal Part

KW - Local Chart

KW - Vector Field

UR - http://www.scopus.com/inward/record.url?scp=85072891626&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-31564-0_2

DO - 10.1007/978-3-642-31564-0_2

M3 - Chapter

AN - SCOPUS:85072891626

SN - 9783642315633

T3 - Lecture Notes in Mathematics

SP - 9

EP - 17

BT - Diffeomorphisms of Elliptic 3-Manifolds

PB - Springer Verlag

ER -

Diffeomorphisms and Embeddings of Manifolds

Abstract

Publication series

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this