This is a BMS basic course taught in English.

## Lecture times and rooms

Lecture | Mon 10:15–13:45 (with breaks) | MA 141 | Prof. John M. Sullivan |

Tutorials | Thu 10:15–11:45 or Fri 10:15–11:45 | MA 651 MA 850 | Max Krause |

## Course topics

- Point-set topology: basic definitions, theorems, and examples
- Covering spaces and the fundamental group: group actions, deck transformations, classification and existence of covering spaces, van Kampen theorem
- Homology: Hurewicz theorem, Eilenberg–Steenrod axioms, simplicial and singular homology, fixed point theorems

## Course work

There will be weekly homework assignments, to be done in groups of two, and handed in before the tutorials (i.e., Thursday or Friday at 10).

Criteria to obtain a Schein: 50% of the homework points and successful completion of a midterm test. There will be a final oral exam. The homework, midterm and final exam may be completed in either German or English.

## News

There was a **mistake in homework sheet 3**, exercise 2. The statements are only to be proven in the case n >= 2. The homework sheet has been amended accordingly.

The **office hours** on Wednesday, November 21, are **cancelled**. Please reach out via mail if you have any questions that week.

## Contact information and office hours

Prof. John M. Sullivan | MA 802 | sullivan@math.tu-berlin.de | TBA |

Max Krause | MA 804 | krause@math.tu-berlin.de | Wed 13 - 15 |

## Midterm Exam

The midterm exam will take place on **Monday, December 10, from 10:15 - 11:45 in room MA 042**. Please be there 15 minutes early. There will be a lecture from 12:15 - 13:45 that day in the usual room MA 141.

You may bring a single DIN A4 (or smaller) sheet of paper with handwritten notes on both sides to the exam.

## Homework

Homework sheet 1

Homework sheet 2

Homework sheet 3

Homework sheet 4

Homework sheet 5

## Literature

Our primary textbook will be Allen Hatcher, *Algebraic Topology*, Cambridge University Press

available online here.

Additional textbooks include:

- James Munkres,
*Topology*, Pearson - William Fulton,
*Algebraic Topology*, GTM 153, Springer - Glen E. Bredon,
*Topology and Geometry*, GTM 139, Springer

- Klaus Jänich,
*Topologie*, Springer - Tammo tom Dieck,
*Topologie*, de Gruyter - Wolfgang Lück,
*Algebraische Topologie*, Vieweg