The Eleventh Week: The Group of Covering Transformations

Michio Kuga

A chapter in Galois’ Dream: Group Theory and Differential Equations, 1993, pp 70-74 from Springer

Abstract: Abstract Let f : D’ → D be a covering. We say that points P 1 and P 2 of D’ are conjugate if f(P 1) = f(P 2). The number of points which are conjugate to P 1 (including P 1 itself) is equal to n = deg(f). Similarly, we say that curves C 1’and C2’ are conjugate if they are lifts of the same curve. In order to construct a curve starting at P 2 which is conjugate to a curve C 1’ starting at P 1, first we project C 1’ to make a curve C. Then take the lift of C which starts at P 2. The number of curves conjugate to C l’ (including C l’ itself) in D’ is also equal to n = deg(f).

Date: 1993
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:978-1-4612-0329-2_12

Ordering information: This item can be ordered from
http://www.springer.com/9781461203292

DOI: 10.1007/978-1-4612-0329-2_12

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 ().