Filtered screens and augmented Teichm\"uller space
Douglas J. LaFountain, R. C. Penner

TL;DR
This paper introduces a new bordification of the decorated Teichmüller space using filtered screens, providing a CW decomposition of the augmented space with a novel indexing by partially oriented stratum graphs.
Contribution
It develops a new bordification of decorated Teichmüller space via filtered screens and characterizes conditions for short curves, leading to a CW decomposition of the augmented space.
Findings
Identifies conditions for paths to produce vanishing length curves.
Constructs a quotient space with a CW decomposition.
Introduces partially oriented stratum graphs as an indexing tool.
Abstract
We study a new bordification of the decorated Teichm\"uller space for a multiply punctured surface F by a space of filtered screens on the surface that arises from a natural elaboration of earlier work of McShane-Penner. We identify necessary and sufficient conditions for paths in this space of filtered screens to yield short curves having vanishing length in the underlying surface F. As a result, an appropriate quotient of this space of filtered screens on F yields a decorated augmented Teichm\"uller space which is shown to admit a CW decomposition that naturally projects to the augmented Teichm\"uller space by forgetting decorations and whose strata are indexed by a new object termed partially oriented stratum graphs.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
