From Hyperbolic Dehn Filling to Surgeries in Representation Varieties

Georgios Kydonakis ()
Additional contact information
Georgios Kydonakis: Alexander von Humboldt-Stiftung

Chapter Chapter 6 in In the Tradition of Thurston II, 2022, pp 201-260 from Springer

Abstract: Abstract Hyperbolic Dehn surgery and the bending procedure provide two ways which can be used to describe hyperbolic deformations of a complete hyperbolic structure on a 3-manifold. Moreover, one can obtain examples of non-Haken manifolds without the use of Thurston’s Uniformization Theorem. We review these gluing techniques and present a logical continuity between these ideas and gluing methods for Higgs bundles. We demonstrate how one can construct certain model objects in representation varieties Hom π 1 Σ , G $$\text{Hom} \left ( \pi _{1} \left ( \Sigma \right ), G \right ) $$ for a topological surface Σ and a semisimple Lie group G. Explicit examples are produced in the case of Θ-positive representations lying in the smooth connected components of the SO p , p + 1 $$\text{SO} \left (p,p+1 \right )$$ representation variety.

Keywords: Hyperbolic Dehn surgery; Character variety; Higher Teichmüller space; Higgs bundle; Parabolic structure; Elliptic operator; Primary: 53C07; Secondary: 14H60, 58D27 (search for similar items in EconPapers)
Date: 2022
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-97560-9_6

Ordering information: This item can be ordered from
http://www.springer.com/9783030975609

DOI: 10.1007/978-3-030-97560-9_6

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().