Fundamental groups of moebius strip and cylinder

Reference no: EM13124329

Show that the Mobius strip and the cylinder both have fundamental group Z.

We can use the following theorem:

If G acts on X, pi1(X) = {e}, and for all x elements of X there exists Ux neighborhood of X such that Ux intersection g(Ux) = empty set for all g elements of G{e}, then pi1(XG) is homeomorphic to G.

Reference no: EM13124329

Questions Cloud

Amount of accumulated depreciation : Calculate the amount of accumulated depreciation to be debited or credited in the preparation of the 2009 consolidated balance sheet.

Use of linear kinematic equations : Two trains are driving towards each other .One at 144 km/h and the other at 72 km/h When they see each other they start to brake at 1 m/ss. There is 950m between them

Solving for systems of linear equations : Create a system of linear equations from my own life. Keep in mind that a system of linear equations will consist of two equations using the same variables and the variables will represent the same thing for both equations

Illustrate what is the probable type of behavior that each : Illustrate what is the probable type of behavior that each of the costs exhibits? The company expects to produce 10,000 caps this month. Would you expect each type of cost to increase or decrease? Why? Can the total cost of 10,000 caps be determi..

Fundamental groups of moebius strip and cylinder : If G acts on X, pi1(X) = {e}, and for all x elements of X there exists Ux neighborhood of X such that Ux intersection g(Ux) = empty set for all g elements of G{e}, then pi1(XG) is homeomorphic to G.

Equivalence of two definitions of contractible space : We have defined space X to be contractible in two ways: Show that these two definitions are equivalent.

What are some of the ways that financial information : The CEO of your company has requested that you prepare a written presentation to be given at the next board of directors meeting regarding the continuing impact that the information age has on financial accounting.

Annotation assignments : annotation Assignments

Linear systems of equations with matrices : From the following augmented matrix, first write the system of equations that represents the augmented matrix and then create a real-world word problem that would represent these equations and their unknowns.

User Account

All Pages