By A. Lahiri

This quantity is an introductory textual content the place the subject material has been awarded lucidly so that it will aid self examine through the newcomers. New definitions are by means of compatible illustrations and the proofs of the theorems are simply available to the readers. adequate variety of examples were included to facilitate transparent knowing of the thoughts. The booklet starts off with the elemental notions of type, functors and homotopy of constant mappings together with relative homotopy. primary teams of circles and torus were taken care of besides the basic team of overlaying areas. Simplexes and complexes are awarded intimately and homology theories-simplicial homology and singular homology were thought of besides calculations of a few homology teams. The publication can be best suited to senior graduate and postgraduate scholars of varied universities and institutes.

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**Sample text**

Existence off* gives thatf(l) g(l). Since f * is closed, we also have f(O) g(O). 11. So,f- g. 11. This gives that f* null path. g is homotopic to a EXERCISES I. In R2 let A = ((x, y) : x = 0, - 1 Sy S I} and B = ((x, y) : 0 < x S l, y =cos nix}. Show that F = A u B is connected but not path connected. 32 ALGEBRAIC TOPOLOGY 2. In R2 let A = {(x, y) : 0 ~ x ~ l, y = xln, n e N} and B= {

A contractible space has trivial fundamental group. A path connected space with trivial fundamental group has a special name. 3. A space is said to be simply connected if it is path connected and has trivial fundamental group for any point. 4. A contractible space is simply connected. The converse is not true. 5. e. of C). We generalise these concepts to any dimension n for n > 1. For the sake of simplicity, we consider the generalisation only to the absolute homotopy groups and not relative homotopy groups.

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