Full Text Available
Note: Clicking the button above will open the full text document at the original institutional repository in a new window.
Euler Classes and Frobenius Algebras
Thesis (MSc)--Stellenbosch University, 2019.
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | en_ZA |
| Published: |
Stellenbosch : Stellenbosch University
2019
|
| Subjects: | |
| Tags: |
No Tags, Be the first to tag this record!
|
| _version_ | 1867613783207182336 |
|---|---|
| access_status_str | Open Access |
| author | Ranaivomanana, Valimbavaka Hosana |
| author2 | Bartlett, Bruce |
| author_browse | Bartlett, Bruce Ranaivomanana, Valimbavaka Hosana |
| author_facet | Bartlett, Bruce Ranaivomanana, Valimbavaka Hosana |
| author_sort | Ranaivomanana, Valimbavaka Hosana |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MSc)--Stellenbosch University, 2019. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/105881 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:41:37.777Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2019 |
| publishDateRange | 2019 |
| publishDateSort | 2019 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/105881 Euler Classes and Frobenius Algebras Ranaivomanana, Valimbavaka Hosana Bartlett, Bruce Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Division Mathematics. De Rham cohomology Frobenius algebras Euler classes Rham, Georges de Algebraic topology UCTD Thesis (MSc)--Stellenbosch University, 2019. ENGLISH ABSTRACT : This thesis investigates the relationship between the handle element of the De Rham cohomology algebra of a compact oriented smooth manifold, thought of as a Frobenius algebra, and the Euler class of the manifold. In this way it gives a complete answer to an exercise posed in the monograph of Kock [5] (which is based on a paper of Abrams [6]), where one is asked to show that these two classes are equal. Firstly, an overview of De Rham cohomology, Thom and Euler classes of smooth manifolds, Poincaré duality, Frobenius algebras, and their graphical calculus is given. Finally, it is shown that the handle element and the Euler class are indeed equal for even-dimensional manifolds. However, they are not equal for odd-dimensional manifolds. AFRIKAANSE OPSOMMING : Hierdie proefskrif ondersoek die verband tussen die handvatselelement van die De Rham-kohomologie-algebra van ’n kompakte georiënteerde gladde variëteit, beskou as ’n Frobenius-algebra, en die Euler-klas van die variëteit. Op hierdie manier gee dit ’n volledige antwoord op ’n oefening wat in die monografie van Kock [5] gebaseer is (wat gebaseer is op ’n papier van Abrams [6]), waar een gevra word om te wys dat hierdie twee klasse gelyk is. Eerstens word ’n oorsig gegee van De Rham-kohomologie, Thom- en Euler-klasse van gladde manifolds, Frobenius algebras, en hul grafiese notasie word gegee. Ten slotte word getoon dat die handvatsel en die Euler-klas inderdaad gelyk is vie ewe-dimensionele variëteite. Maar hulle is nie gelyk nie vir onewe-dimensionele variëteite nie. 2019-03-05T12:41:05Z 2019-04-17T08:17:03Z 2019-03-05T12:41:05Z 2019-04-17T08:17:03Z 2019-04 Thesis http://hdl.handle.net/10019.1/105881 en_ZA Stellenbosch University vii, 66 pages application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | De Rham cohomology Frobenius algebras Euler classes Rham, Georges de Algebraic topology UCTD Ranaivomanana, Valimbavaka Hosana Euler Classes and Frobenius Algebras |
| title | Euler Classes and Frobenius Algebras |
| title_full | Euler Classes and Frobenius Algebras |
| title_fullStr | Euler Classes and Frobenius Algebras |
| title_full_unstemmed | Euler Classes and Frobenius Algebras |
| title_short | Euler Classes and Frobenius Algebras |
| title_sort | euler classes and frobenius algebras |
| topic | De Rham cohomology Frobenius algebras Euler classes Rham, Georges de Algebraic topology UCTD |
| url | http://hdl.handle.net/10019.1/105881 |
| work_keys_str_mv | AT ranaivomananavalimbavakahosana eulerclassesandfrobeniusalgebras |