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An Introduction to the Fundamental Group and some Applications

Al-Abdallah, Abdel Rahman LU (2013) In Master's Theses in Mathematical Sciences MATM01 20132
Mathematics (Faculty of Sciences)
Abstract
This thesis provides a self-contained introduction to the Fundamental Group and presents some of its applications, such as Brouwer fixed point Theorem,the Game of Hex, Nielsen-Schreier Theorem, the van-Kampen Theorem and some of its consequences, Borsuk-Ulam Theorem and some of its applications,the Jordan curve Theorem, and some other examples and applications.Some results in Group Theory will be introduced as necessary, in order to study the van-Kampen Theorem, which plays a key role in our proof of the Jordan Curve Theorem.
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author
Al-Abdallah, Abdel Rahman LU
supervisor
organization
course
MATM01 20132
year
type
H2 - Master's Degree (Two Years)
subject
keywords
fundamental group, homotopy, brouwer, game of hex, nielsen shreier, free group, van kampen, torus knot, covering space, covering transformations, borsuk ulam, ham sandwich, pancake sandwich, jordan curve
publication/series
Master's Theses in Mathematical Sciences
report number
LUNFMA-3080-2013
ISSN
1404-6342
other publication id
2013:E61
language
English
id
4222932
date added to LUP
2014-02-14 16:13:35
date last changed
2014-02-14 16:13:35
@misc{4222932,
  abstract     = {This thesis provides a self-contained introduction to the Fundamental Group and presents some of its applications, such as Brouwer fixed point Theorem,the Game of Hex, Nielsen-Schreier Theorem, the van-Kampen Theorem and some of its consequences, Borsuk-Ulam Theorem and some of its applications,the Jordan curve Theorem, and some other examples and applications.Some results in Group Theory will be introduced as necessary, in order to study the van-Kampen Theorem, which plays a key role in our proof of the Jordan Curve Theorem.},
  author       = {Al-Abdallah, Abdel Rahman},
  issn         = {1404-6342},
  keyword      = {fundamental group,homotopy,brouwer,game of hex,nielsen shreier,free group,van kampen,torus knot,covering space,covering transformations,borsuk ulam,ham sandwich,pancake sandwich,jordan curve},
  language     = {eng},
  note         = {Student Paper},
  series       = {Master's Theses in Mathematical Sciences},
  title        = {An Introduction to the Fundamental Group and some Applications},
  year         = {2013},
}