By John Harer, Arnold Kas, Robion Kirby

ISBN-10: 0821823515

ISBN-13: 9780821823514

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**Extra resources for Handlebody Decompositions of Complex Surfaces**

**Sample text**

Y- , mod 4 Given integers ,Y Pick a base point based at * * in C1P which generate and loops 0L ,. . ,Y. ,c } with fiber T 1 r , i < i< P ; 6 J , 1 < j

57 We will construct in sections 3 and 4. L(2k+1;2) as well as (a,b) = 1, have the sme homotopy type as the Kummer surface L(a,b;2), S?. We will also construct handlebody decompositions of these surfaces in sections 3 and 4. 25 and the language of framed links (§0), we are ready to give a handlebody decomposition of the half Kummer surface be easy to see the Kummer surface characteristic Let and the other elliptic surfaces of Euler 12T. ~. 1. 1 N n = IT (D.. 2. The attaching spheres of each 1-handle are opposite each other, and the framing of the 2 1 2-handle is zero.

If V - V V oo where V oo is a V . V y 2 = x L 3 - t 11 . In this bounds a 4-ball. to an elliptic surface (except for the singular V - V consists of a cusp fiber over °°, and a section, - 2 . If we perturb the equation, the compactifi- cation can be done equivariantly, and surface. L with one cusp point and with self intersection is a homology sphere, and it is unknown that V 5 - t . which meets the first one transversely and which in now with self intersection 3 V, then the "added part" is defined by the equation: Here we can compoactify = x °° which is a fiver of type II (a cusp fiber) -1 V 2 is the plumbing manifold graph (see §0, appendix), and is compactified to an elliptic surface consists of the fiber over 0 V y (2,3,11) V = V^ fl V, homology sphere L is an elliptic K3 lies in an elliptic K3 f surface as the boundary of a neighborhood of a cusp fiber together with a section.

### Handlebody Decompositions of Complex Surfaces by John Harer, Arnold Kas, Robion Kirby

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Categories: Algebraic Geometry