30.10.2009 in Regensburg

1. Homotopy theoretical language

1. weak equivalence; spectra; limits and colimits

1. Uli Bunke

06.11.3009 in Augsburg

2. Simplicial objects

2. simplicial sets and spaces; geometric realisation; classifying spaces of categories

2. Marc Nieper-Wißkirchen

27.11.2009 in Regensburg

3. Thom-Pontrjagin construction

4. Sheaftheory

3. Thom spaces and Thom spectra; Thom-Pontrjagin construction; topology of MO, MSO and MU

4. sheaves of sets and spaces; stalks; topologies

3. Emanuel Scheidegger

4. Franz Vogler

04.12.2009 in München

4. Sheaftheory

5. Quasitopological spaces

4. sheaves of sets and spaces; stalks; topologies

5. definition; limits and colimits in QTop; homotopy theory [Ayala 2.6 - 2.8]

4. Franz Vogler

5. Christian Blohmann

11.12.2009 in Augsburg

6. Equivariant sheaves

7. Geometric cobordism category

6. manifolds as topological category; equivariant sheaves; fiberwise sheaves; examples [Ayala 2.9-2.21]

7. definition; formulation of the theorem [Ayala chapter 3]

6. Uli Bunke

7. Dmytro Shklyarov

8.1.2010 in München

8. Summary of proof

9. Proof of Ayala's lemma 4.4.3

8. introduction of intermediate objects; strategy [Ayala 4.1-4.4]

8. Ansgar Schneider

9. Bernhard Hanke

15.1.2010 in Regensburg

10. Ayala chapter 4.5

11. Ayala chapter 4.8

12. Proof of Ayala's lemma 4.7.1

10. Sven Führing

11. Marco Hien

12. Nadine Große

22.1.2010 in Regensburg

13. Applications

14. Applications

15. Perspectives

13. stable families of manifolds, the classical GMTW-theorem

14. applications of immersions and embeddings

13. Sven Führing

14. Bernd Ammann

15. David Ayala