Mathematics > Geometric Topology
arXiv:2601.05102 (math)
[Submitted on 8 Jan 2026 (v1), last revised 22 May 2026 (this version, v2)]
Abstract:We develop the theory of $\Theta$-positive representations from general Fuchsian groups to linear groups over real closed fields. Our definition, which does not assume the boundary map to be continuous, encompasses many generalizations of positive or Anosov representations that have been considered in the literature.
| Comments: | 106 pages. Added a conjecture on flag varieties with a positive structure (Conjecture 1.6), proved this conjecture in some cases (Section 3.9) and improved some theorems conditionally to this conjecture (Theorem H, Section 4.6, Corollary 7.5) |
| Subjects: | Geometric Topology (math.GT); Algebraic Geometry (math.AG); Differential Geometry (math.DG); Representation Theory (math.RT) |
| MSC classes: | 22E40, 30F60, 14P10 |
| Cite as: | arXiv:2601.05102 [math.GT] |
| (or arXiv:2601.05102v2 [math.GT] for this version) | |
| https://doi.org/10.48550/arXiv.2601.05102 arXiv-issued DOI via DataCite |
Submission history
From: Nicolas Tholozan [view email]
[v1]
Thu, 8 Jan 2026 16:48:13 UTC (101 KB)
[v2]
Fri, 22 May 2026 13:37:07 UTC (110 KB)
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