Jump to ContentJump to Main Navigation
Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)$
Users without a subscription are not able to see the full content.

Paula Tretkoff

Print publication date: 2016

Print ISBN-13: 9780691144771

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691144771.001.0001

Show Summary Details
Page of

PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2020. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in PRSO for personal use.date: 19 February 2020

Topological Invariants and Differential Geometry

Topological Invariants and Differential Geometry

(p.6) Chapter One Topological Invariants and Differential Geometry
Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

Paula Tretkoff

Princeton University Press

This chapter deals with topological invariants and differential geometry. It first considers a topological space X for which singular homology and cohomology are defined, along with the Euler number e(X). The Euler number, also known as the Euler-Poincaré characteristic, is an important invariant of a topological space X. It generalizes the notion of the cardinality of a finite set. The chapter presents the simple formulas for computing the Euler-Poincaré characteristic (Euler number) of many of the spaces to be encountered throughout the book. It also discusses fundamental groups and covering spaces and some basics of the theory of complex manifolds and Hermitian metrics, including the concept of real manifold. Finally, it provides some general facts about divisors, line bundles, and the first Chern class on a complex manifold X.

Keywords:   topological invariant, differential geometry, Euler number, fundamental group, covering space, complex manifold, Hermitian metric, divisor, line bundle, first Chern class

Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.