تقرير
Scissors automorphism groups and their homology
| العنوان: | Scissors automorphism groups and their homology |
|---|---|
| المؤلفون: | Kupers, Alexander, Lemann, Ezekiel, Malkiewich, Cary, Miller, Jeremy, Sroka, Robin J. |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - K-Theory and Homology, Mathematics - Algebraic Topology, Mathematics - Group Theory, 18F25, 19D99, 20J05, 55P42, 52B45 |
| الوصف: | In any category with a reasonable notion of cover, each object has a group of scissors automorphisms. We prove that under mild conditions, the homology of this group is independent of the object, and can be expressed in terms of the scissors congruence K-theory spectrum defined by Zakharevich. We therefore obtain both a group-theoretic interpretation of Zakharevich's higher scissors congruence K-theory, as well as a method to compute the homology of scissors automorphism groups. We apply this to various families of groups, such as interval exchange groups and Brin--Thompson groups, recovering results of Szymik--Wahl, Li, and Tanner, and obtaining new results as well. Comment: 58 pages, 16 figures. Comments welcome! v2: Corrected examples 6.35-37, updated references |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2408.08081 |
| رقم الأكسشن: | edsarx.2408.08081 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |