(a) Let C be a path component of X and let zo E C be a...

Transcribed Image Text:

(a) Let C be a path component of X and let zo E C be a basepoint. Show that the inclusion map CX induces an isomorphism of fundamental groups (C, o) (X, xo). (b) Let p: X X be a simply connected covering space. Let A CX be path-connected and locally path-connected, and let A be a path component of p-(A). Then show that pla A A is a covering space corresponding to the kernel of the homomorphism T(A) (X). (a) Let C be a path component of X and let zo E C be a basepoint. Show that the inclusion map CX induces an isomorphism of fundamental groups (C, o) (X, xo). (b) Let p: X X be a simply connected covering space. Let A CX be path-connected and locally path-connected, and let A be a path component of p-(A). Then show that pla A A is a covering space corresponding to the kernel of the homomorphism T(A) (X).

Answer rating: 100% (QA)

The detailed ... View the full answer