VL: Topology, WS 21/22

This is a BMS Basic Course, which will thus be given in English (in the classroom and online), the tutorials will take place in the classrom.

ATTENTION: Due to the worse COVID-19 situation at the beginning of 2022 all lectures and tutorials are now moved to zoom.

VL:	Monday	10-12	H 3004
	Wednesday	10-12	(zoom)
Tut:	Tuesday	10-12	MA 550
	Thursday	14-16	MA 850

DEFAULT DATE FOR ORAL EXAM: TUESDAY; FEBRUARY 15, 2022. Please send an email to Antje Schulz (aschulz@math.tu-berlin.de) to register.

There will also be opportunities to take the exam later. Yet, after Feb 15 all remaining oral exams will be queued together with remaining exams from other courses. Typically once a month there will be day for taking such oral exams. If you want to register for one of those, please also send an email to Antje Schulz. You will be notified about options as soon as they will arise. And then you will be able to choose if you want to take that exam or if you want to wait again for the next opportunity.

Teaching assistent: Holger Eble. See his page for the exercise sessions.

Contents

The course roughly follows a mix of the book by Armstrong and other sources. Topics include:

• Introduction
• Continuity
• Compactness and connectedness
• Identification spaces
• The fundamental group
• Triangulations
• Surfaces
• Simplicial homology
• Persistent homology
• Morse matchings

Software/Visualization

• homology computation in polymake
• persistent homology in polymake
• persistent homology example

References

1. M.A. Armstrong: Basic topology, Springer (1983).
2. J. Dugundji: Topology, Allyn and Bacon (1966).
3. R. Forman: A user's guide to discrete Morse theory, Semin. Loth. Combin. (2002).
4. D. Gale: The game of Hex and the Brouwer fixed-point theorem, Amer. Math. Monthly 86 (1979).
5. M. Gessen: Perfect Rigour: A Genius and the Mathematical Breakthrough of a Century, HarperCollins (2009).
6. H. Edelsbrunner, J.L. Harer: Computational topology, AMS (2010)
7. A. Hatcher: Algebraic topology, Cambridge (2002).
8. M. Joswig: Computing invariants of simplicial manifolds, unpublished (2004).
9. D. Kozlov: Combinatorial algebraic topology, Springer (2008).
10. C. Manolescu: Pin(2)-equivariant Seiberg-Witten Floer homology and the triangulation conjecture, J. Amer. Math. Soc. 29 (2016).
11. E. Ossa: Topologie, Mathematik, Vieweg, 2. Auflage (2009).

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Last modified: Mo Aug 08 07:42:40 UTC 2022 by mic