# Algebraic topology by C. R. F. Maunder

By C. R. F. Maunder

Thorough, glossy therapy, basically from a homotopy theoretic perspective. issues contain homotopy and simplicial complexes, the basic team, homology thought, homotopy concept, homotopy teams and CW-Complexes and different subject matters. every one bankruptcy comprises routines and proposals for additional interpreting. 1980 corrected variation.

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**Example text**

As a means of making Condition (ii) more precise, one could restrict to the case that ???? is indecomposable. Another variation is to restrict to the Jacobians of smooth curves. 7]. 2. The original motivation for this nonexistence expectation was the following. Let ????(????????) (????, ????) denote the statement: There exists an Abelian variety ???? of dimension ???? defined over ???? which is not isogenous to the Jacobian of any curve of compact type; (here, this is an isogeny of Abelian varieties without polarization).

W. Bosma, J. Cannon and C. Playoust, The Magma algebra system. I. The user language, J. Symbol. Comput. 24, pp. 235–265, 1997. V. G. Drinfeld and S. G. Vladut, The number of points of an algebraic curve (translated from the Russian paper in Funktsional. Anal. i Prilozhen), Functional Anal. Appl. 17, pp.

Finding a uniformizing element ????0 of ????(????0 (????2 + ????)) and expressing ????0 and ????1 in it, we find ????0 = (????30 + (????2 + ????)????0 + (????2 + ????))3 ????0 (????0 + ????)2 (????0 + ???? + 1)2 and ????1 = (????30 + (????2 + ????)????20 + (????2 + ????)2 )3 . ????40 (????0 + ????)2 (????0 + ???? + 1)2 To find ????????2 +???? (????, ????), we need to factor a bivariate polynomial of ????-degree 9. 2 does not apply, though it still predicts the existence of one factor of ????degree 1. The factors turn out to be ???????? + ????2 + ???? , ????2 ????2 + ????????2 ???? + (????2 + ????)???????? + (????3 + ????2 )???? + ????2 ????2 + ????4 + ????2 , ????2 ????2 + (???? + 1)????2 ???? + (????2 + ????)???????? + (????3 + ????)???? + (????2 + 1)????2 + ????4 + ????2 , and ????4 ????3 + ????4 ????2 + (????2 + ????)????4 ???? + (????2 + ????)????3 ????2 + (????2 + ????)????3 ???? + (????4 + ????2 )????3 + (????2 + ???? + 1)????2 ????3 + (????4 + ????2 )????2 ???? + (????4 + ????2 )????2 + (????2 + ????)????????3 + (????4 + ????)????????2 + (????6 + ????5 + ????4 + ????3 )???? + ????4 .