Multiplicative structure in the stable splitting of ΩSLn(C)
| Autor: | Jeremy Hahn, Allen Yuan |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Conjecture
Wedge sum General Mathematics 010102 general mathematics Multiplicative function Structure (category theory) Affine Grassmannian (manifold) Space (mathematics) Mathematics::Algebraic Topology 01 natural sciences Combinatorics 0103 physical sciences Loop space 010307 mathematical physics 0101 mathematics Complex cobordism Mathematics |
| Zdroj: | Advances in Mathematics. 348:412-455 |
| ISSN: | 0001-8708 |
| DOI: | 10.1016/j.aim.2019.03.022 |
| Popis: | The space of based loops in S L n ( C ) , also known as the affine Grassmannian of S L n ( C ) , admits an E 2 or fusion product. Work of Mitchell and Richter proves that this based loop space stably splits as an infinite wedge sum. We prove that the Mitchell–Richter splitting is coherently multiplicative, but not E 2 . Nonetheless, we show that the splitting becomes E 2 after base-change to complex cobordism. Our proof of the A ∞ splitting involves on the one hand an analysis of the multiplicative properties of Weiss calculus, and on the other a use of Beilinson–Drinfeld Grassmannians to verify a conjecture of Mahowald and Richter. Other results are obtained by explicit, obstruction-theoretic computations. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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