1549055384-Symplectic_Geometry_and_Topology__Eliashberg_

Lecture 4. The Symplectic Case, Part I Let X be a closed smooth 4-manifold with b~ > 1. Suppose that X has a symplectic form ...

128 M. HUTCHINGS AND C .H. TAUBES, SEIBERG-WITTEN EQUATIONS 4.2. The canonical Spine structure An w-compatible almost complex st ...

LECTURE 4. THE SYMPLECTIC CASE, PART I 129 With the preceding understood, we can write '!/; = (~) with a E C^00 ( E) and (3 E n° ...

130 M. HUTCHINGS AND C. H. TAUBES, SEIBERG-WITTEN EQUATIONS Now we come to the point. Consider an arbitrary Spine structure with ...

LECTURE 4. THE SYMPLECTIC CASE, PART I 131 4.5. Step 3: Uniqueness of the solution For the canonical Spine structure, a is just ...

132 M. HUTCHINGS AND C. H. TAUBES, SEIBERG-WITTEN EQUATIONS Now comes a key step, where we bring in cohomological information ab ...

LECTURE 4. THE SYMPLECTIC CASE, PART I 133 where z is a new constant which is still independent of r. Putting (4.20) and (4.21) ...

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Lecture 5. The Symplectic Case, Part II We will now discuss the Seiberg-Witten invariant on a symplectic manifold X (with b! > ...

136 M. HUTCHINGS AND C. H. TAUBES, SEIBERG-WITTEN EQUATIONS 5.2. Motivation Fix e with [w] · e > 0. Suppose SW(e) -I 0. Then ...

LECTURE 5. THE SYMPLECTIC CASE, PART II 137 We can go beyond Theorem 5.1 to show that the Seiberg-Witten invariant SW(e) is equa ...

138 M. HUTCHINGS AND C. H. TAUBES, SEIBERG-WITTEN EQUATIONS We say that a curve C C X together with a set De C C of d points is ...

Then we define LECTURE 5. THE SYMPLECTIC CASE, PART II 1 !+,o = 1 -t' ! +,1=l+t, l+t !+,2 = 1 + t2' f - (1 + t)(l - t^2 ) +,3 - ...

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BIBLIOGRAPHY M. F. Atiyah, R. Bott, and A. Shapiro, Clifford modules, Topology 3 (1964) suppl. 13-38. N. Berline, E. Getzler, a ...

142 M. HUTCHINGS AND C. H. TAUBES, SEIBERG-WITTEN EQUATIONS C. H. Taubes, Counting curves and connections, preprint. E. Witten, ...

Lectures on Floer Homology Dietmar Salamon ...

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IAS/Park City Mathematics Series Volume 7, 1999 Lectures on Floer Homology Dietmar Salamon Introduction The purpose of these lec ...

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