1549055384-Symplectic_Geometry_and_Topology__Eliashberg_

IAS/Park City Mathematics Series Volume 7, 1999 Euler Characteristics and Lagrangian Intersections Mikhail Grinberg and Robert M ...

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LECTURE 1 1.1. The Centerpiece Theorem The main result of these lectures is the following. Theorem. Let X be an oriented real al ...

270 M. GRINBERG AND R. MACPHERSON, EULER CHARACTERISTICS near the smaller stratum, which assure that the topology of S is locall ...

LECTURE 1. 271 1.4. The Euler characteristic of a constructible function Let X be a real algebraic manifold, and S be a stratifi ...

272 M. GRINBERG AND R. MACPHERSON, EULER CHARACTERISTICS 1.5. Homology n-product of cycles The next ingredient of Theorem 1.1 we ...

LECTURE l. 273 The multiplicities are assigned as follows. We identify T* X with JR^2 in the natural way. For x E X, not a point ...

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Lecture 2. 2.1. The conormal variety to a stratification In this lecture we introduce the two remaining ingredients of Theorem 1 ...

276 M. GRINBERG AND R. MACPHERSON, EULER CHARACTERISTICS (a) For any point a E A, and a sequence {bi } (i = 1, 2, ... ) of point ...

LECTURE 2. 277 Show that the covector dy is not generic at the origin, but that any covector not proportional to dy is. The foll ...

278 M. GRINBERG AND R. MACPHERSON, EULER CHARACTERISTICS Exercise 2.5.1. Show that the multiplicity m~Z is equal to x(f'), where ...

Lecture 3. 3.1. Classical Morse theory In this lecture we begin the proof of Theorem 1.1. We start by discussing t he case when ...

280 M. GRINBERG AND R. MACPHERSON, EULER CHARACTERISTICS Assuming now that g is Morse, we find that Ax nAx =Ax n {dg} = l_)-1)&g ...

LECTURE 3. 281 as the pair (N n B, n g-^1 [-8, +oo[N n B, n 9 -^1 (-8)), where the notation is as in Section 2.4. Note that the ...

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Lecture 4. 4.1. Standard pairs We will be somewhat sketchy in the rest of the proof of Theorem 1.1. However, all of the things w ...

284 M. GRINBERG AND R. MACPHERSON, EULER CHARACTERISTICS Note that the pair (Y, Z) contains all the information necessary to rec ...

LECTURE 4. 285 4.3. Fary functors Up until now, we have been developing a kind of a calculus of Euler characteristics. In partic ...

286 M. GRINBERG AND R. MACPHERSON, EULER CHARACTERISTICS (Recall that each standard pair (yt, Zt) must be transverse to S.) Then ...