تقرير
Foams with flat connections and algebraic K-theory
| العنوان: | Foams with flat connections and algebraic K-theory |
|---|---|
| المؤلفون: | Gepner, David, Im, Mee Seong, Khovanov, Mikhail, Kitchloo, Nitu |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - K-Theory and Homology, Mathematics - Algebraic Topology, Mathematics - Geometric Topology, Primary: 57R90, 19B99, 19D06, 18M05, Secondary: 19A99, 55N22 |
| الوصف: | This paper proposes a connection between algebraic K-theory and foam cobordisms, where foams are stratified manifolds with singularities of a prescribed form. We consider $n$-dimensional foams equipped with a flat bundle of finitely-generated projective $R$-modules over each facet of the foam, together with gluing conditions along the subfoam of singular points. In a suitable sense which will become clear, a vertex (or the smallest stratum) of an $n$-dimensional foam replaces an $(n+1)$-simplex with a total ordering of vertices. We show that the first K-theory group of a ring $R$ can be identified with the cobordism group of decorated 1-foams embedded in the plane. A similar relation between the $n$-th algebraic K-theory group of a ring $R$ and the cobordism group of decorated $n$-foams embedded in $\mathbb{R}^{n+1}$ is expected for $n>1$. An analogous correspondence is proposed for arbitrary exact categories. Modifying the embedding and other conditions on the foams may lead to new flavors of K-theory groups. Comment: 57 pages, many figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2405.14465 |
| رقم الأكسشن: | edsarx.2405.14465 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |