A basic course in algebraic topology - download pdf or read online

By Massey

ISBN-10: 038797430X

ISBN-13: 9780387974309

This publication is meant to function a textbook for a direction in algebraic topology before everything graduate point. the most issues lined are the type of compact 2-manifolds, the basic workforce, masking areas, singular homology conception, and singular cohomology concept. those subject matters are built systematically, keeping off all unecessary definitions, terminology, and technical equipment. at any place attainable, the geometric motivation in the back of a number of the strategies is emphasised. The textual content contains fabric from the 1st 5 chapters of the author's prior publication, ALGEBRAIC TOPOLOGY: AN creation (GTM 56), including just about all of the now out-of- print SINGULAR HOMOLOGY thought (GTM 70). the cloth from the sooner books has been conscientiously revised, corrected, and taken modern.

Show description

Read or Download A basic course in algebraic topology PDF

Best algebraic geometry books

Byrnes B. (Ed)'s Computational Noncommutative Algebra and Applications PDF

The fusion of algebra, research and geometry, and their software to genuine global difficulties, were dominant subject matters underlying arithmetic for over a century. Geometric algebras, brought and categorized by means of Clifford within the past due nineteenth century, have performed a admired position during this attempt, as visible within the mathematical paintings of Cartan, Brauer, Weyl, Chevelley, Atiyah, and Bott, and in purposes to physics within the paintings of Pauli, Dirac and others.

Download e-book for iPad: A Scrapbook of Complex Curve Theory (University Series in by C. Herbert Clemens

This high quality booklet through Herb Clemens quick turned a favourite of many advanced algebraic geometers whilst it used to be first released in 1980. it's been well-liked by rookies and specialists ever on account that. it really is written as a publication of "impressions" of a trip throughout the concept of advanced algebraic curves. Many issues of compelling good looks ensue alongside the best way.

Get Semidefinite optimization and convex algebraic geometry PDF

This e-book presents a self-contained, obtainable advent to the mathematical advances and demanding situations because of using semidefinite programming in polynomial optimization. This speedy evolving examine region with contributions from the varied fields of convex geometry, algebraic geometry, and optimization is named convex algebraic geometry.

Extra resources for A basic course in algebraic topology

Example text

1) 0 ˇ ˇ i Di D : 0 i D1 Let f W „ ! B a projective family with dim B D 1, „ smooth and K „b ample for all b 2 B. Further let X D „b0 for some b0 2 B a singular fiber and let W ‡ ! „ P X D Xz C riD1 i Fi where be an embedded resolution of X Â „. Finally let Y D Xz is the strict transform of X and F i are exceptional divisors for . We are interested in finding conditions that ˇ are necessary for K Y to remain ample (cf. 6)). Let Ei WD Fi ˇXz be the exceptional divisors for W Xz ! X and for simplicity ˇof computation, assume that the E i are irreducible.

Show that if f W Y ! X / is a divisor on X and G is a divisor on Y , then Chapter 2. 1) If D is big (resp. 2) If D is big (resp. pseudo-effective) and F is effective and its support contains all f -exceptional divisors, then f 1 D C F is big (resp. 3) Show that if G G 0 , then f G f G 0 . Deduce from this that if G is big (resp. 4) Give an example where G is not big, but f G is big. 12. X / such that Di 0, D1 Q D2 and D1 ^ D2 D 0. D 3 / has a multiple which is mobile. 13. X /. Show that if k is minimal, then r 1 ; : : : ; rk are linearly independent over Q.

As this ˇ computation is local near P the only relevant issue about ˇ the ampleness of KXz C E ˇXz is whether it is ample in a neighbourhood of E X WD E ˇXz . K Xz C EX / EX is positive. 4. Let Z be a smooth projective surface with non-negative Kodaira dimension and € Z an effective divisor. K Z C €/ C > 0 for every proper curve C Z, then KZ C € is ample. Chapter 3. d 3/ as EX is isomorphic to a plane curve of degree d . Again, we obtain the same condition as above and thus conclude that K ‡0 is ample if and only if d > 3.

Download PDF sample

A basic course in algebraic topology by Massey


by Steven
4.3

Rated 4.17 of 5 – based on 44 votes