An Introduction to the Fundamental Group and some Applications
(2013) In Master's Theses in Mathematical Sciences MATM01 20132Mathematics (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.
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/4222932
- author
- Al-Abdallah, Abdel Rahman LU
- supervisor
-
- Arne Meurman LU
- organization
- course
- MATM01 20132
- year
- 2013
- 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}}, language = {{eng}}, note = {{Student Paper}}, series = {{Master's Theses in Mathematical Sciences}}, title = {{An Introduction to the Fundamental Group and some Applications}}, year = {{2013}}, }