Titlebook: Stratified Morse Theory; Mark Goresky,Robert MacPherson Book 1988 Springer-Verlag Berlin Heidelberg 1988 Area.Dimension.Homotopy.Levi form

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Nonproper Morse Functions as a dense open subset. For example, . may be a compactification of some noncompact algebraic variety . ⊂ ., and . may be a smooth function defined on the ambient .. We shall assume that it is possible to find a stratification of . so that . ⊂ . is a union of strata. Thus, . is obtained from . by r

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Salivary-Gland

Relative Morse TheoryMorse function seem to end in failure because one loses curvature estimates on the Morse index of .. Instead, we are forced to “relativize” the Morse theory of .. Our main result is stated in Sect. 9.8.

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The Topology of Complex Analytic Varieties and the Lefschetz Hyperplane Theoremf a Stein manifold is bounded by its complex dimension. In this section of the introduction, we give a sketch of the statements of the theorems with motivation and some history. Technically precise statements of the theorems in their most general form are grouped together in Chapter 1 of Part II of the book.

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conformity

Fringed Setsuadrant in ℝ. whose closure contains a segment of the .-axis ending at the origin, and which are unions of vertical segments. Fringed sets of this type will appear throughout the technical discussions in Part I.

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Introductione stratum . of complex codimension . in .. Let λ denote the Morse index of . | . at the point ., and let .=. (.) be the associated critical value. We will consider the Morse theory of . | ., where . = . − .. Suppose the interval [., .] contains no critical values of . . other than ., and that .∈(., .).