The signature group for paths of higher variation as an inverse limit

29.04.2026, 11:00 Uhr  –  Campus Golm, Building 9, Room 2.22 and via Zoom
Arbeitsgruppenseminar Analysis

Felix Medwed (Universität Potsdam)

E. Le Donne and R. Züst (2021) showed that the space of signatures of rectifiable paths is a geodesic metric tree. We extend their result originally formulated in terms of curve length to the setting of $p$-variation for $p>1$. This extension relies on results of Boedihardjo, Geng, Lyons, and Yang (2016) concerning signatures of weakly geometric rough paths, which provide the appropriate analytical control in the $p$-variation framework. The key components of the original construction are reinterpreted using the language of metric groups, allowing us to define and work with the signature group adapted to $p$-variation. Within this framework, we revisit the lifting procedure introduced by Le Donne and Züst—namely, the construction of a canonical lift of a path into a suitable group structure—and show that the main result, concerning the existence and properties of such lifts, continues to hold when length is replaced by $p$-variation.

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