M8130 Algebraic topology, tutorial 10, 2020 9. 12. 2020 Exercise 1. Compare nn(X,x0) and nn(X, xi), when distinguished points (are / are not) path connected. .v. fur y - s4 u d: \ 1 1 /J- - — 1 \ Figure 2 Figure 1 ■fan <*> AltottM. i-c a**- it.) At, M'lt <4U UT ***** f 1—) £ • w -z- t ' -(Ttihs r—tfôfc- _Y//// xjgr_ fn\ ar %—t *4 —?*2. 4r*Z : ^ J —x—— —'— —I *---•—•--•--1 ľ / V < X T„ '^ř / N \ / v á a r 1 1 ! *-^—-1---—t /í J AJ 0 i f ^ ^ fy t tX%>^- F. N M8130 Algebraic topology, tutorial 10, 2020 9. J 2. M8130 Algebraic topology, tutorial 10, 2020 9. 12. 2020 Exercise 2. Using Van Kampen Theorem compute the fundamental group of the sphere with k holes. HlUiVl UaV f*U /»okf*4 *i az St/ tw I-5> l_ fleUUtw £/) ,, ( -1 a.-1 - A / M8130 Algebraic topology, tutorial 10, 2020 9. 12. 2020 Exercise 4. Using Van Kampen Theorem compute the fundamental group of the sphere to which k Moebius bands are attached. \ [ ot^d tUsAo ])J-1----? '- - ^fc t"1 *ta/t IP2- ~-->-1 Ä j / / /, JT d ////{j J--- My rŕ tL — I A ttA i--V> ^ t 2- 1--> f1 ď