Homotopy and the Fundamental Group

Question 1

Define Homotopy

Answer 1

Question 2

Is homotopy an equivalence relation?

Answer 2

Yes

Question 3

Define null homotopic

Answer 3

Question 4

Define homotopic equivalence

Answer 4

Question 5

Is homotopic equivalence an equivalence relation?

Answer 5

Yes

Question 6

Define contracible

Answer 6

Question 7

Define the cone on X

Answer 7

Question 8

Is a contracible space path connected?

Answer 8

Question 9

Give the relationship between homotopy and homeomorphic

Answer 9

Question 10

Define a based space /map

Answer 10

Question 11

Define a loop

Answer 11

Question 12

When are loops homotopic

Answer 12

Question 13

The define the concatenation of loops

Answer 13

Question 14

Define the funadmental group

Answer 14

Question 15

Is two based maps are homotopic then

Answer 15

Question 16

Define f_*

Answer 16

Question 17

Going from f to f_* preserves?

Answer 17

Question 18

Is based spaces are homotopy equivalent then?

Answer 18

Question 19

In a path connected space, what do we know about the based spaces

Answer 19

Question 20

A space is contractible then what can we say about its fundamental group

Answer 20

Question 21

Define simply connected

Answer 21

Question 22

In a convex subset of R^n what can we say about paths in it?

Answer 22

Question 23

State Brouwer’s fixed point theorem

Answer 23