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

We have made more dates available for oral exams. Please check the link below if you need to schedule one. Remember that you need to register for the oral exam at least one week prior to taking it.

Oral final exams will be offered Feb. 19 and 21, and Apr. 2 and 4.

## Contact information and office hours

Prof. John M. Sullivan | MA 802 | sullivan@math.tu-berlin.de | Tue 13 - 14 |

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.

Results

Note: The threshold for passing has been altered to 40% of the total points. If your result does not appear on the list, please contact Max.

## Practice test

## Homework

Homework sheet 1

Homework sheet 2

Homework sheet 3

Homework sheet 4

Homework sheet 5

Homework sheet 6

Homework sheet 7

Homework sheet 8

Homework sheet 9

Homework sheet 10

Homework sheet 11

Homework sheet 12

Homework sheet 13

## 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