Versionen im Vergleich

Alte Version 61

changes.mady.by.user Albert Haase

Gespeichert am

verglichen mit

Neue Version 62

changes.mady.by.user Albert Haase

Gespeichert am

Schlüssel

  • Diese Zeile wurde hinzugefügt.
  • Diese Zeile wurde entfernt.
  • Formatierung wurde geändert.

...

  • The tutorial next Monday will be postponed to 24 Feb at 10 AM (details of where we meet will follow)
  • Here's a list of speakers for Wednesday (11 Feb)

Christoph Horst (Topological quotients, CW complexes)

Arthur Jacot (Degree, properties)

Albert (CW homology, cellular boundary formula)

Reimer Backhaus (Tor and Ext)

Markus Penner (Homology with coefficients, UCT)

Myriam Mahaman (Cohomology, UCT)

Talks are 25 minutes long. If you have questions please email Albert or go to his office hours on Monday.
Hinweis
titleWritten Exams

The first written exam will take place on March 3 from 2-4 PM in "Großer Hörsaal Informatikgebäude Takustraße 9".

The second written exam will take place on April 13 from 10AM - 12PM in "Seminarraum Animallee 2".

There will be no further written exams administered by us. Oral exams need to be scheduled directly with Prof. Blagojevic.

Hinweis
titleTalks February 4th

On Tuesday, Feb 24 at 10 AM in the SR in Arnimallee 2 we will hold a preparatory tutorial for the written exams. Exercises that will be discussed during the tutorial will appear online by Feb 20.

 

 

 

 

 

Bereich

Course Description

 

We understand this course as a comprehensive beginners course in algebraic topology. Although it is helpful to have taken Topologie I to follow the present course, it is not necessary. The aim of Topologie II is for you to thoroughly understand and be able to apply all notions of homology and cohomology, the cup and cross product, as well as some results on duality (for instance Poincaré duality). The course will roughly be structured as follows (as time permits):

  • Categories and functors, chain complexes

  • Singular homology, chain homotopy

  • Mayer-Vietoris Sequence, Jordan Curve Theorem

  • Reduced homology, relative homology, Alexander's theorem

  • Simplicial homology

  • Degrees, Euler characteristic, Lefschetz number, Lefschetz fixed point theorem

  • CW complexes

  • Cellular homology

  • Eilenberg–Steenrod axioms

  • Künneth Theorem

  • Universal Coefficient Theorem

  • Singular cohomology, simplicial cohomology

  • Cup product

  • Cross product, topological manifolds

  • Poincaré Duality

  • Alexander Duality

  • Manifolds with boundary

We recommend the books by J. Munkres ("Elements of Algebraic Topology", Addison-Wesley 1984) and A. Hatcher ("Algebraic Topology", Cambridge U Press 2002, also online) and the succinct lecture notes by J. P. May ("A Concise Course in Algebraic Topology", online).

...