E-Book, Englisch, Band 2030, 240 Seiten, eBook
Reihe: Lecture Notes in Mathematics
Matsumoto / Montesinos-Amilibia Pseudo-periodic Maps and Degeneration of Riemann Surfaces
Erscheinungsjahr 2011
ISBN: 978-3-642-22534-5
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, Band 2030, 240 Seiten, eBook
Reihe: Lecture Notes in Mathematics
ISBN: 978-3-642-22534-5
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
The first part of the book studies pseudo-periodic maps of a closed surface of genus greater than or equal to two. This class of homeomorphisms was originally introduced by J. Nielsen in 1944 as an extension of periodic maps. In this book, the conjugacy classes of the (chiral) pseudo-periodic mapping classes are completely classified, and Nielsen's incomplete classification is corrected. The second part applies
the results of the first part to the topology of degeneration of Riemann surfaces. It is shown that the set of topological types of all the singular fibers appearing in one parameter holomorphic families of Riemann surfaces is in a bijective correspondence with the set of conjugacy classes of the pseudo-periodic maps of negative twists. The correspondence is given by the topological monodromy.
Zielgruppe
Research
Autoren/Hrsg.
Weitere Infos & Material
Part I: Conjugacy Classification of Pseudo-periodic Mapping Classes.- 1 Pseudo-periodic Maps.- 2 Standard Form.- 3 Generalized Quotient.- 4 Uniqueness of Minimal Quotient.- 5 A Theorem in Elementary Number Theory.- 6 Conjugacy Invariants.- Part II: The Topology of Degeneration of Riemann Surfaces.- 7 Topological Monodromy.- 8 Blowing Down Is a Topological Operation.- 9 Singular Open-Book.
