Discussion Overview
The discussion centers on the integer cohomology of the infinite-dimensional Grassmann manifold of real unoriented k-planes in Euclidean space. Participants are particularly interested in computing the Bockstein exact sequence for a specific coefficient sequence and exploring the relationship between Stiefel-Whitney classes and integer classes.
Discussion Character
- Exploratory, Technical explanation, Debate/contested
Main Points Raised
- One participant expresses difficulty in finding resources on the Z cohomology of the infinite-dimensional Grassmann manifold.
- Another participant suggests that the topic may be covered in Milnor and Stacheff's work, but questions whether it includes Z cohomology.
- A later reply indicates uncertainty, stating that only Z2 cohomology seems to be available upon further checking.
- There is a suggestion that classifying spaces might be relevant to the discussion.
- One participant confirms that classifying spaces are used but notes that they can only find Z2 cohomology for the Grassmann manifold of unoriented planes.
Areas of Agreement / Disagreement
Participants do not appear to reach a consensus on the availability of Z cohomology information for the infinite-dimensional Grassmann manifold, with multiple views on the coverage in existing literature and the relevance of classifying spaces.
Contextual Notes
There are limitations regarding the availability of resources on Z cohomology and the specific focus on Z2 cohomology, which may affect the completeness of the discussion.