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Contains complete bookmarked desk of contents and numbered pages. this is often an development of a duplicate to be had during the Library Genesis undertaking. the actual Stillwell translation is dated July 31, 2009.
John Stillwell was once the recipient of the Chauvenet Prize for Mathematical Exposition in 2005. The papers during this ebook chronicle Henri Poincaré's trip in algebraic topology among 1892 and 1904, from his discovery of the basic team to his formula of the Poincaré conjecture. For the 1st time in English translation, you can stick to each step (and occasional stumble) alongside the way in which, with assistance from translator John Stillwell's creation and editorial reviews. Now that the Poincaré conjecture has eventually been proved, through Grigory Perelman, it sort of feels well timed to gather the papers that shape the heritage to this recognized conjecture. Poincaré's papers are in truth the 1st draft of algebraic topology, introducing its major material (manifolds) and simple recommendations (homotopy and homology). All mathematicians drawn to topology and its heritage will get pleasure from this ebook. This quantity is one in all a casual series of works in the heritage of arithmetic sequence. Volumes during this subset, "Sources", are classical mathematical works that served as cornerstones for contemporary mathematical inspiration.
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Extra resources for Homotopy Equivalences of 3-Manifolds with Boundaries
Of) t = glS 1 × O must be (a m u l t i p l e of) k I = glO × S I. We argue a n a l o g o u s l y Let G to a map of a tube into Precisely ~Q~e end-point o_~f k 4 , 1 Q corollary. since as in Case i. (M,~), F, M lies in a curve of f-iF. (M,m),= and i__ss aspherical. d. 9. Let f: is admissibly (G~) deformed + in (M~m) be (M~) so that the number of curves of f-iF is as small as possible. Then fiG: (G,~) ~ surface obtained Proof. 9. Thus, that fIGl is inessential in if splitting a__t f-IF. of essential (GI,~I) (M,~)~ then (G,~) is the curves in is a c o m p o n e n t (GI~I) (G~), of and (G,~) such must be either a 46 square, or an annulus.
In (M,~). Then, by definition, g: (D,~) ~ (M,~) such that and that the r e s t r i c t i o n essential deformation in (D,~). g singular curve in of g i__n ( M ~ ) ~ (D,~) + if and (M,m) such i i 3, g- 1 F is equal to one side in F. Therefore let F be inessential is an i-faced disc, to one side~ k, of F. sinqular disc g: that and useful g curves is chosen so that it has the above proper- in addition, the number of components of g -I F is as small as possible. Assume g-iF ~ k. Then there exists at least one curve, kl, of g-iF w h i c h is d i s j o i n t (DI,~I) ~ from (D,d)= such that glkl cannot be essential instead of (DI,~I) ~ and applying in k.
2. E v e r y curve of f-iF is e s s e n t i a l in 3. If the r e s t r i c t i o n o__f f an admissible o___f f G. t__o every c o m p o n e n t o__f G sinqular square, (M~m) w h i c h is e s s e n t i a l in Remark. 4 can be g e n e r a l i z e d to essential maps. Proof. 1-3. :8 Proposition. Let (M,m) be an irreducible 3-manifold. b e an a d m i s s i b l e surface in o_f F Let F (M~m), w i t h F n 5M = 5F~ b u t no c o m p o n e n t ~ 2-sphere or an i-faced disc, the m a n i f o l d o b t a i n e d bv splittinq 1 i i i 3.