تقرير
The cohomology of homogeneous spaces in historical context
| العنوان: | The cohomology of homogeneous spaces in historical context |
|---|---|
| المؤلفون: | Carlson, Jeffrey D. |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Topology, Mathematics - History and Overview, Mathematics - K-Theory and Homology, 55-03, 57T15, 57T35, 16U80 (Primary), 01A60, 01A61, 57T30 (Secondary) |
| الوصف: | The real singular cohomology ring of a homogeneous space $G/K$, interpreted as the real Borel equivariant cohomology $H^*_K(G)$, was historically the first computation of equivariant cohomology of any nontrivial connected group action. After early approaches using the Cartan model for equivariant cohomology with real coefficients and the Serre spectral sequence, post-1962 work computing the groups and rings $H^*(G/K)$ and $H^*_H(G/K)$ with more general coefficient rings motivated the development of minimal models in rational homotopy theory, the Eilenberg-Moore spectral sequence, and A-infinity algebras. In this essay, we survey the history of these ideas and the associated results. Comment: A shortened version to appear in the Contemp. Math. volume Group Actions and Equivariant Cohomology. A longer version should appear on the arXiv eventually. 31 pp. Comments welcome |
| نوع الوثيقة: | Working Paper |
| الوصول الحر: | http://arxiv.org/abs/2312.02014Test |
| رقم الانضمام: | edsarx.2312.02014 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |