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Monday, May 18, 2020 | History

7 edition of Fundamental Groups and Covering Spaces found in the catalog.

Fundamental Groups and Covering Spaces

by Elon Lages Lima

  • 108 Want to read
  • 2 Currently reading

Published by AK Peters .
Written in English

    Subjects:
  • Mathematics,
  • Fundamental groups (Mathematic,
  • Science/Mathematics,
  • General,
  • Covering spaces (Topology),
  • Topology - General,
  • Algebraic topology,
  • Fundamental groups (Mathematics)

  • Edition Notes

    ContributionsJonas Gomes (Translator)
    The Physical Object
    FormatHardcover
    Number of Pages230
    ID Numbers
    Open LibraryOL8690688M
    ISBN 101568811314
    ISBN 109781568811314

    The Fundamental Group of a Topological Space Lecture 13 (Febru ) Lecture 14 (Febru ) Lecture 15 (Febru ) Covering Maps Lecture 16 (Febru ) Lecture 17 (Febru ) Lecture 18 (Febru ) Free Discontinuous Group Actions on Topological Spaces Lecture 19 (March 6, ) Lecture 20 (March 9. THEORY OF COVERING SPACES BY SAUL LUBKIN Introduction. In this paper I study covering spaces in which the base space is an arbitrary topological space. No use is made of arcs and no assumptions of a global or local nature are required. In consequence, the fundamental group ir(X, Xo) which we obtain fre-.

    Proposition (fundamental group criterion for existence of lifting): Let p: Z → Y {\displaystyle p:Z\to Y} be a covering and let f: X → Y {\displaystyle f:X\to Y} be a continuous function, where X {\displaystyle X} is path-connected and strongly locally connected. The Fundamental Group and Covering Spaces In the first seven chapters we have dealt with point-set topology. This chapter pro-vides an introduction to algebraic topology. Algebraic topology may be regarded as the study of topological spaces and continuous functions by means of algebraic objects such as groups and homomorphisms.

      Book. TOC. Actions. Share. Topology: Point‐Set and Geometric. Author(s): and metric spaces—Topology covers the construction of spaces from other spaces, including products and quotient spaces. This innovative text culminates with topics from geometric and algebraic topology (the Classification Theorem for Surfaces and the fundamental.   We motivate the notion of covering spaces and give the definition and some basic examples. For notes, see here: ~ucahjde/tg/ht.


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Fundamental Groups and Covering Spaces by Elon Lages Lima Download PDF EPUB FB2

The text is interspersed with over 70 illustrative examples and over 50 well-drawn explanatory pictures. Overall, the book is clearly written and has a good flow to it and succeeds admirably in the task it set itself."" -Philip Maynard, The Mathematical Gazette, July "Cited by:   Fundamental Groups and Covering Spaces Pages pages This introductory textbook describes fundamental groups and their topological soul mates, the covering spaces.

The author provides several illustrative examples that touch upon different areas of mathematics, but in keeping with the books introductory aim, they are all quite by: Fundamental Groups and Covering Spaces by Elon Lages Lima () on *FREE* shipping on qualifying offers.

Fundamental Groups and Covering Spaces. Book Description This introductory textbook describes fundamental groups and their topological soul mates, the covering spaces. The author provides several illustrative examples that touch upon different areas of mathematics, but in keeping with the books introductory aim, they are all quite elementary.

Download Fundamental group and covering spaces: the facts. Intro. book pdf free download link or read online here in PDF. Read online Fundamental group and covering spaces: the facts.

Intro. book pdf free download link book now. All books are in clear. The fundamental group of a space is one of the central topological invariants we can de ne. We begin with necessary background material on the subject, building to the de nition of the fundamental group.

For a hands-on calculation, we compute ˇ. 1(S1). This, by design, introduces the idea of cov- ering Size: KB. Covering Spaces and Calculation of Fundamental Groups. Covering Spaces. 33 1. Definition of Covering Let X, B topological spaces, p: X → B a continuous map.

Assume that p is surjective and each point of B possesses a neighborhood U such that the preimage p−1(U) of U is a disjoint union of open sets Vαand p maps each Vαhomeomorphically onto Size: KB. ily of pointed fundamental groups, which we denote π1top(X) //X, whose fibers are canonically πtop 1 (X,x).

π1top(X)is a group object among covering spaces. We call it the fundamental group family. (It is also the isotropy group of the fundamental groupoid, asFile Size: KB.

Fundamental group is important for at least two reasons. The first is the connection to covering spaces. Cite this chapter as: Schwarz A.S. () The Fundamental Group and Covering Spaces. In: Topology for Physicists.

Grundlehren der mathematischen Wissenschaften (A Series of Comprehensive Studies in Mathematics), vol Author: Albert S. Schwarz. CHAPTER 2 Basic properties and examples of covering spaces The main topic of the rst part of this book is as follows. Definition Let Xbe a topological space.A covering space of X(or just cover for short) is a space X equipped with a continuous mape f: Xe!Xsuch that the following holds for all x2 X.

There exists a neighborhood Uof xsuch that f 1(U) is the disjoint union. Ross Geoghegan in his review (MR) of two papers by M.A. Armstrong on the fundamental groups of orbit spaces wrote: "These two papers show which parts of elementary covering space theory carry over from the free to the nonfree case.

Cite this chapter as: Fulton W. () The Fundamental Group and Covering Spaces. In: Algebraic Topology. Graduate Texts in Mathematics, vol Author: William Fulton. Try the new Google Books. Check out the new look and enjoy easier access to your favorite features Exercises on the fundamental group and covering spaces.

Peter J. Kahn. - Mathematics - 84 called Choose commutative diagram Conclude conjugacy class connected 1-complex consider maps f countably covering equivalence covering.

An accomplished example of the algebraic topologist's dream come true, covering spaces are a geometric (that is, topological) structure that is completely characterized by its algebraic counterpart.

The author provides several illustrative examples that touch upon different areas of mathematics, but in keeping with the book's introductory aim, they are all quite elementary. The elementary character of fundamental groups and covering spaces are presented as suitable for introducing algebraic topology.

The two topics are treated in separate sections. The focus is on the use of algebraic invariants in topological problems. Fundamental Groups and Covering Spaces Elon Lages Lima AK Peters ISBN Poincar´e has been described as one of the last great universalists, being the most pro-lific author of his time, surpassed only by Euler in quantity: his legacy permeates many areas of contemporary mathematics.

Algebraic topology is one of these, and hisCited by: is a platform for academics to share research papers. The Fundamental Group, Covering Spaces and Topology in Biology Conference Paper (PDF Available)   September   with   Reads  How we measure 'reads' A 'read' is counted each time someone.

Introduction To Topology. This book explains the following topics: Basic concepts, Constructing topologies, Connectedness, Separation axioms and the Hausdorff property, Compactness and its relatives, Quotient spaces, Homotopy, The fundamental group and some application, Covering spaces and Classification of covering space.

Author(s): Alex Kuronya. fundamental groupoid of a topological space and use them to classify covering spaces. Contents 1. Homotopy theory of paths and loops1 Change of base point and unbased homotopies4 2.

Covering spaces 5 3. The fundamental group of the circle, spheres, and lense spaces8 Applications of ˇ 1(S1) 9 4. The van Kampen theorem10 File Size: KB.Universal covering spaces and fundamental groups in algebraic geometry as schemes parRavi Vakil etKirsten Wickelgren Résumé.

En topologie, les notions du groupe fondamental et du revêtement universel sont lieés l’une à l’autre. En suivant l’exemple topologique, on. In Homotopy Theory we defined the fundamental group of a topological space as the group of equivalence classes of “loops” on the space.

In this post, we discuss the fundamental group from another point of view, this time making use of the concept of covering doing so, we will uncover some interesting analogies with the theory of Galois groups (see Galois Groups).