Please put [Lecture Geometry and topology] as the subject.

- Second semester students in Mathematics interested in a mixture of (linear) geometry and discrete mathematics, but everyone is welcome.

- The lecture.
- Monday 10:00-11:00, Thursday 09:00-10:00, Friday 09:00-10:00.
- Starting 7th week, ending 12th week.
- Carslaw Lecture Theatre 275 and online via zoom.

- Tutorials.
- Friday 13:00-14:00.
- Starting 8th week, ending 13th week.
- Carslaw Seminar Room 350.

- Material for the lecture.
- There is a script [Hi11] available via Canvas that the lecture will follow. Additional literature (not mandatory but recommendations only). The recommended literature from the course outline is [Ad94], [Bl67] and [FiGa91]. The lecture sometimes takes a different perspective and I sometimes borrow the exposition from [Ba10], [BoMu08], [BrHa12], [We96] or [Wi96] for graphs, and from [A+21], [FaSt96] and [Ka93] for surfaces and knots
- Prerecorded lectures on the “What is...algebraic topology?” and “What is...geometric topology?” (twice: as mini lectures and the real lectures) playlists here: Click

- Summary: Click
- Mini presentation: Click
- The detailed plan: Click
- All slides: Click

**Speaker**: Daniel Tubbenhauer,**Topic**: Basics about graphs - Graphs, subdivision, trees, Eulerian circuits**Slides**: Click**Speaker**: Daniel Tubbenhauer,**Topic**: Surfaces I - Various surfaces, homeomorphism, Euler characteristic**Slides**: Click**Speaker**: Daniel Tubbenhauer,**Topic**: Surfaces II - Invariance under subdivision, cutting and pasting, orientation**Slides**: Click**Speaker**: Daniel Tubbenhauer,**Topic**: Surfaces III - Classification of surfaces**Slides**: Click**Speaker**: Daniel Tubbenhauer,**Topic**: Graphs and surfaces - Graphs on surfaces, planar graphs**Slides**: Click**Speaker**: Daniel Tubbenhauer,**Topic**: Knots - Knots diagrams, knot coloring, Seifert surfaces**Slides**: Click**Speaker**: Daniel Tubbenhauer,**Topic**: Geometric topology - recap**Slides**: Click

- Exercise 7, Click, Solutions: Click
- Exercise 8, Click, Solutions: Click
- Exercise 9, Click, Solutions: Click
- Exercise 10, Click, Solutions: Click
- Exercise 11, Click, Solutions: Click
- Exercise 12, Click, Solutions: Click

- [Ad94] C.C. Adams. The knot book. An elementary introduction to the mathematical theory of knots. Revised reprint of the 1994 original. American Mathematical Society, Providence, RI, 2004. xiv+307 pp.
- [A+21] Edited by C. Adams, E. Flapan, A. Henrich, L.H. Kauffman, L.D. Ludwig and S. Nelson. Encyclopedia of knot theory. CRC Press, Boca Raton, FL, [2021], @2021. xi+941 pp.
- [Ba10] R.B. Bapat. Graphs and matrices. Universitext. Springer, London; Hindustan Book Agency, New Delhi, 2010. x+171 pp.
- [Bl67] D.W. Blackett. Elementary topology. A combinatorial and algebraic approach. Academic Press, New York-London 1967 ix+224 pp.
- [BoMu08] J.A. Bondy, U.S.R. Murty. Graph theory. Graduate Texts in Mathematics, 244. Springer, New York, 2008. xii+651 pp.
- [BrHa12] A.E. Brouwer, W.H. Haemers. Spectra of graphs. Universitext. Springer, New York, 2012. xiv+250 pp.
- [FaSt96] D.W. Farmer, T.B. Stanford. Knots and surfaces. A guide to discovering mathematics. Mathematical World, 6. American Mathematical Society, Providence, RI, 1996.
- [FiGa91] P.A. Firby, C.F. Gardiner. Surface topology. A guide to discovering mathematics. Second edition. Ellis Horwood Series: Mathematics and its Applications. Ellis Horwood, New York; distributed by Prentice Hall, Inc., Englewood Cliffs, NJ, 1991. 220 pp.
- [Hi11] J. Hillman. Topology. Lecture notes for the Topology component of Geometry and Topology. Available via Canvas.
- [Ka93] L.H. Kauffman. Knots and physics. Second edition. World Scientific Publishing Co., Inc., River Edge, NJ, 1993. xiv+723 pp.
- [We96] D.B. West. Introduction to graph theory. Prentice Hall, Inc., Upper Saddle River, NJ, 1996. xvi+512 pp.
- [Wi96] R.J. Wilson. Introduction to graph theory. Fourth edition. Longman, Harlow, 1996. viii+171 pp.