Lecturer, TA |

- Monday 12-14
- Thursday 17-19

- Monday 14:45-15:45
- Thursday 16:05-17:05

- Homotopy, Homotopy type, deformation retracts.
- The idea of functors and categories.
- The fundamental group of the circle and of the spheres.
- Applications: (n=2) Brouwer fixed point theorem , The Borsuk-Ulam Theorem, The fundamental theorem of algebra.
- Siefert-van-Kampen Theorem. Applications.
- The ABC of surfaces: Torus, Projective plane, Moebuis strip, Klien bottle. What is Oreintability.
- Covering spaces.
- Higher Homotopy groups.
- Classification of Surfaces.
#### Homology Theory

- Definition and baseic properties:
- Mayer-Vietoris Sequence.
- Jordan Curve theorem.
- Brouwer fixed point theorem, invariance of dimension, invariance of domain.
- degree of a map.
- CW complexes.
#### Manifolds their Geometry and Toplogy.

- Topological and Smooth manifolds. Sard's theorem and approximation with smooth maps.
- Tangent spaces. Vector bundles, fiber bundles.
- Embedding theorems, immersions.
- Applications: Robotics and complexity.
- Applications: What is the shape of the universe.

- A. Hatcher, Algebraic Topology.
- Bredon, Topology and Geometry, GTM 139, Springer.

Avraham Aizenbud's website

Tahl Novik's website

Yair Glazner's webpage

The book in Hebrew

Notes From A course by Varshavsky

The Syllabus is here.

Exercise 1 part a,
Exercise 1 part b,
Exercise 1 bonus.
Submit by Nov. 12, 2015.

Exercise 2