Computing chow rings of classifying spaces from representation rings / von Alexander Ziegler. Wuppertal, 2026
Inhalt
- Acknowledgements
- Chapter 1. Introduction
- 1.1. Group Cohomology, Classifying Spaces and Chow Rings
- 1.2. Computations
- 1.3. Utilizing the -Filtration and Computer Algebra
- 1.4. Universal Polynomials
- 1.5. Main Results
- 1.6. Structure of this Thesis
- Chapter 2. Definitions and Computational Tools
- 2.1. Group Cohomology and Chow Rings of Classifying Spaces
- 2.2. Filtrations on the Representation Ring
- 2.3. Motivic Cohomology and the Motivic Atiyah–Hirzebruch Spectral Sequence
- 2.4. Controlling the Chow Ring in high Degree
- 2.5. Universal Polynomials
- Chapter 3. The Modulo 2 Chow Ring of B(Syl2GL(4,2))
- 3.1. The Chow Ring of a Dihedral Group
- 3.2. Towards detecting Cycles on a Family of Subgroups of `3́9`42`"̇613A``45`47`"603ASyl2GL(4,2)
- 3.3. The Main Computation
- Chapter 4. A Chow Ring not generated by Chern Classes
- Chapter 5. Computing Integral Chow Rings
- 5.1. Groups of Order 12
- 5.2. Groups of Order 16
- 5.3. Groups of Order 18
- 5.4. Groups of Order 21
- 5.5. Groups of Order 24
- 5.6. Groups of Order 27
- Chapter 6. Outlook
- 6.1. Yagita's Conjecture on *(BG)MU*(BG)
- 6.2. Transferred Euler Classes
- 6.3. Groups of p-rank at most 2
- 6.4. Counterexamples to the Chow–Künneth Formula
- Appendix A. Restricting Topological Cycles of B(Syl2GL(4,2))
- Appendix B. Characters, their Restrictions and the Restrictions of their Chern Classes
- Appendix C. Universal Polynomials
- Appendix D. SAGE and GAP code
- Bibliography