Algebraic Topology MTH 477 For Master of Mathematics

Algebraic Topology MTH 477 For Master of Mathematics By Dr. SOHAIL IQBAL Assistant Professor Department of Mathematics, CIIT Islamabad MTH 477 -Algebraic Topology by Dr Sohail Iqbal 1

Previous lecture Relative Singular Homology Ø Deformation retract Ø Reduced homology (cont. ) Ø Excision Ø Mayer-Vietoris theorem Ø Applications Source: http: //www. faculty. idc. ac. il/arik/site/skeletonbased. asp MTH 477 -Algebraic Topology by Dr Sohail Iqbal 2

Source: http: //www. faculty. idc. ac. il/arik/site/skeletonbased. asp MTH 477 -Algebraic Topology by Dr Sohail Iqbal 3

Free Groups • MTH 477 - Algebraic Topology by Dr Sohail Iqbal 4

Free product of groups • MTH 477 -Algebraic Topology by Dr Sohail Iqbal 5

Free product of groups • MTH 477 -Algebraic Topology by Dr Sohail Iqbal 6

Van Kampen theorem Why we need Van Kampen theorem? MTH 477 -Algebraic Topology by Dr Sohail Iqbal 7

Van Kampen theorem • MTH 477 -Algebraic Topology by Dr Sohail Iqbal 8

Van Kampen theorem • MTH 477 -Algebraic Topology by Dr Sohail Iqbal 9

Van Kampen theorem • MTH 477 -Algebraic Topology by Dr Sohail Iqbal 10

Van Kampen theorem • MTH 477 -Algebraic Topology by Dr Sohail Iqbal 11

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Free Groups • MTH 477 - Algebraic Topology by Dr Sohail Iqbal 18

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Equivalence of simplicial and singular homology (an overview) • MTH 477 -Algebraic Topology by Dr Sohail Iqbal 23

Next time Cellular homology MTH 477 -Algebraic Topology by Dr Sohail Iqbal 24 Source: wikipedia

End of the lecture MTH 477 -Algebraic Topology by Dr Sohail Iqbal 25