Uniqueness of real ring spectra up to higher homotopy
| Autor: | Davies, Jack Morgan |
|---|---|
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Ann. K-Th. 9 (2024) 447-473 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.2140/akt.2024.9.447 |
| Popis: | We discuss a notion of uniqueness up to $n$-homotopy and study examples from stable homotopy theory. In particular, we show that the $q$-expansion map from elliptic cohomology to topological $K$-theory is unique up to $3$-homotopy, away from the prime $2$, and that upon taking $p$-completions and $\mathbf{F}_p^\times$-homotopy fixed points, this map is uniquely defined up to $(2p-3)$-homotopy. Using this, we prove new relationships between Adams operations on connective and dualisable topological modular forms -- other applications, including a construction of a connective model of Behrens' $Q(N)$ spectra away from $2N$, will be explored elsewhere. The technical tool facilitating this uniqueness is a variant of the Goerss--Hopkins obstruction theory for real spectra, which applies to various elliptic cohomology and topological $K$-theories with a trivial complex conjugation action as well as some of their homotopy fixed points. Comment: 24 pages, comments are always welcome |
| Databáze: | arXiv |
| Externí odkaz: |
|