Question: Consider the closed curve y: [0, 27] C{0} given by y(t) 2 cos 2t + i sin 2t. Prove that y is not contractible

$Consider the closed curve y: [0, 27] C\{0} given by y(t) 2$

Consider the closed curve y: [0, 27] C\{0} given by y(t) 2 cos 2t + i sin 2t. Prove that y is not contractible (i.e. not homotopic to a point) in C\{0}.

Step by Step Solution

★★★★★

3.53 Rating (150 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Given the function g, prove that g is not one-to-one using the definition of a one-to-one function. a. g(x) = 1 - x2 b. g(x) = 3x2 + 1 c. g(x) = x4 - x2 d. (1x) = 1/x6

Prove that it is not possible to determine both wavelength of incident radiation and spacing of reflecting planes in a crystal by measuring the Bragg angles for several orders.

A triple point refers to a point in a PT phase diagram for which three phases are in equilibrium. Do all triple points correspond to a gasliquidsolid equilibrium?

Consider the closed curve y: [0, 27] - C\\ {0} given by y(t) = 2 cos 2t + i sin 2t. Prove that y is not contractible (i.e. not homotopic to a point ) in CHO}

For the following system of equation what are the values of x and z if they exist? 2x + 3y z 1 4x + y 32 11 3x 2y + 52 21

1. (60 pts True/False. Indicate whether the statement is true or false. If the statement is false, present an explanation or counterexample. (No explanation necessary for each true statement.) (2...

sole thus plZ 8. [-/1 Points] DETAILS SCALCET9 13.3.053.EP. Consider the following curve. x = sin(2t), y = -cos(2t), Using the given parametric equations, give the corresponding vector equation r(t)....

1. (1 point) For the given position vectors r(t), compute the (tangent) velocity vector r0 (t) for the given value of t . A) Let r(t) = (cost, sint). , )? Then r0 ( 4 )= ( B) Let r(t) = (t 2 ,t 3 )....

MATLAB sessions: Laboratory 4 MAT 275 Laboratory 4 MATLAB solvers for First-Order IVP In this laboratory session we will learn how to 1. Use MATLAB solvers for solving scalar IVP 2. Use MATLAB...

paper comparing 2 public companies in the same industry (ex. Ford/GM, Jet Blue/Southwest, Nike Under Armour). You will research the companies, industry and perform financial statement analysis to...

Elnora and Partners is a recently formed a partnership of lawyers. The partnership has ten partners (all of whom are practising lawyers) and 15 associate lawyers (lawyers who work for the partnership...

A golf ball is launched at an angle of 20 to the horizontal, with a speed of 60 m/s and a rotation rate of 90 rad/s. Neglecting air drag, determine the number of revolutions the ball makes by the...

How do you perform common operations like adding, removing, or searching elements in these structures?

With what velocity (v) must the ball rotate if the tension in the top rope is twice that of the tension in the bottom rope? L L m

Q:Discuss in detail any IEEE standard and show how it defines further improvement in the field?

A rigid container with a volume of 1m3 is filled with air, due to heat absorption, the pressure of the air increases from 0.1 MPa to 0.15 MPa, and the initial temperature is 20 (when pressure is...

Single selection: The adiabatic rigid closed container filled with air is equipped with an electric heating wire, if the electric heating is turned on, and the air is taken as the system, then ( )....

Q.What is meant by telecom standards and what are the main standard bodies?

Tanner invested $80,000 cash along with office equipment valued at $26,000 in the company in exchange for common stock

Consider the closed curve in the xy-plane given by: x+2x+y4 + 4y = 5. a. Show that dy dx = -(x+1) 2(3+1)* b. Write an equation for the line tangent to the curve at the point (-2, 1). c. Find the...

Consider the closed curve in the x y - plane given by: x 4 + 4 x + y 2 + 2 y = 5 ( a ) ( 2 points ) Show that: d y d x = - 2 ( x 3 + 1 ) y + 1 ( c ) ( 3 points ) Find the coordinates of the two...

Problem 5 (10 points): Consider a closed curve in the plane, that does not self-intersect and has total length (perimeter) P. If A denotes the area enclosed by the curve, prove that p2 > 41A

Let F be defined as in the previous question. Consider the closed curve ( on a unit sphere, as shown in pink in the sketch below, traversed in the direction indicated by the arrows. Which of the...

Free Response Questions - No Calculator 13. Consider the closed curve in the x - y plane given by x?y + 3y3 = 24 a. (2 pts) Find x - 2xy x 2 y' + 2xy + 9424, = 0 * 2+942 y ( x 2 + 94 2 ) 2-214 * 2...

answer all Makeover Inc. believes that at its current stock price of $16.00 the firm is undervalued in the market. Makeover plans to repurchase 2.4 million of its 20 million shares outstanding. The...