On MU-homology of connective models of higher Real K-theories
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913571295723520 |
|---|---|
| author | Carrick, Christian Hill, Michael A. |
| author_facet | Carrick, Christian Hill, Michael A. |
| contents | We use the slice filtration to study the $MU$-homology of the fixed points of connective models of Lubin--Tate theory studied by Hill--Hopkins--Ravenel and Beaudry--Hill--Shi--Zeng. We show that, unlike their periodic counterparts $EO_n$, the $MU$ homology of $BP^{((G))}\langle m\rangle^G$ usually fails to be even and torsion free. This can only happen when the height $n=m|G|/2$ is less than $3$, and in the edge case $n=2$, we show that this holds for $tmf_0(3)$ but not for $tmf_0(5)$, and we give a complete computation of the $MU_*MU$-comodule algebra $MU_*tmf_0(3)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02326 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On MU-homology of connective models of higher Real K-theories Carrick, Christian Hill, Michael A. Algebraic Topology We use the slice filtration to study the $MU$-homology of the fixed points of connective models of Lubin--Tate theory studied by Hill--Hopkins--Ravenel and Beaudry--Hill--Shi--Zeng. We show that, unlike their periodic counterparts $EO_n$, the $MU$ homology of $BP^{((G))}\langle m\rangle^G$ usually fails to be even and torsion free. This can only happen when the height $n=m|G|/2$ is less than $3$, and in the edge case $n=2$, we show that this holds for $tmf_0(3)$ but not for $tmf_0(5)$, and we give a complete computation of the $MU_*MU$-comodule algebra $MU_*tmf_0(3)$. |
| title | On MU-homology of connective models of higher Real K-theories |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2411.02326 |