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From Forsters book the following will be covered:

1.Definitions and elementary properties,pg. 1-13

2.Sheaves, sections.6.1-6.5,pg.40-42

3.Differential forms and integration, pg.59-81,skipping sections 10.5-10.16. Corollary 10.7 was given though, with a direct proof.

4.Compact Riemann surfaces, pg. 96-141. Many of the proofs in ¡ì13 have already been done at the beginning of the course. I don't know if we will have time for proofs in ¡ì17 and I will give information about this later.

All assigments have been graded and put in the shelves on the 7th floor. They were all accepted.

There is an error in part 1) of the assignment. The roles of j and k should be changed in the final part of the statement.

SYLLABUS : The first weeks I lectured from R.Narasimhans book Complex Analysis in One Variable. Here are my lecture notes

Then I covered Chapter 7 (Elliptic functions) and section 8.3 (Picard's theorem) from L.V.Ahlfors book Complex Analysis. You can get a copy from me. Here are my lecture notes from section 7.3 which contain some more details than the book.

Next week we will start from the beginning of O.Forsters book Lectures of Riemann Surfaces. I will come back with more details about what material we cover.

Here is the mandatory assignment

Please hand it in by monday october 31st.