Translator’s Introduction 4

Max Dehn

A chapter in Papers on Group Theory and Topology, 1987, pp 127-132 from Springer

Abstract: Abstract This famous and influential paper is a memorable introduction to topology, combinatorial group theory and noneuclidean geometry. To see Dehn weave these threads into a coherent pattern is an unforgettable demonstration of the unity of mathematics. Of course, there is a historical basis for this coherence in the work of Klein and Poincaré in the 1880’s, and the relation between surface topology and hyperbolic geometry had already been used with considerable sophistication by Poincaré [1904], but Dehn’s paper is the first, I believe, to show equal sophistication in the treatment of combinatorial group theory. In particular, it is the first in which a purely combinatorial algorithm is justified by appeal to the hyperbolic metric.

Keywords: Kleinian Group; Hyperbolic Group; Surface Topology; Hyperbolic Geometry; Combinatorial Algorithm (search for similar items in EconPapers)
Date: 1987
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:978-1-4612-4668-8_7

Ordering information: This item can be ordered from
http://www.springer.com/9781461246688

DOI: 10.1007/978-1-4612-4668-8_7

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 ().