Equivariant $v_{1,\vec{0}}$-self maps
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912284022931456 |
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| author | Balderrama, William Hou, Yueshi Zhang, Shangjie |
| author_facet | Balderrama, William Hou, Yueshi Zhang, Shangjie |
| contents | Let $G$ be a cyclic $p$-group or generalized quaternion group, $X\in π_0 S_G$ be a virtual $G$-set, and $V$ be a fixed point free complex $G$-representation. Under conditions depending on the sizes of $G$, $X$, and $V$, we construct a self map $v\colonΣ^V C(X)_{(p)}\rightarrow C(X)_{(p)}$ on the cofiber of $X$ which induces an equivalence in $G$-equivariant $K$-theory. These are transchromatic $v_{1,\vec{0}}$-self maps, in the sense that they are lifts of classical $v_1$-self maps for which the telescope $C(X)_{(p)}[v^{-1}]$ can have nonzero rational geometric fixed points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15852 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equivariant $v_{1,\vec{0}}$-self maps Balderrama, William Hou, Yueshi Zhang, Shangjie Algebraic Topology Let $G$ be a cyclic $p$-group or generalized quaternion group, $X\in π_0 S_G$ be a virtual $G$-set, and $V$ be a fixed point free complex $G$-representation. Under conditions depending on the sizes of $G$, $X$, and $V$, we construct a self map $v\colonΣ^V C(X)_{(p)}\rightarrow C(X)_{(p)}$ on the cofiber of $X$ which induces an equivalence in $G$-equivariant $K$-theory. These are transchromatic $v_{1,\vec{0}}$-self maps, in the sense that they are lifts of classical $v_1$-self maps for which the telescope $C(X)_{(p)}[v^{-1}]$ can have nonzero rational geometric fixed points. |
| title | Equivariant $v_{1,\vec{0}}$-self maps |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2503.15852 |