Titlebook: Intersection Homology & Perverse Sheaves; with Applications to Laurenţiu G. Maxim Textbook 2019 Springer Nature Switzerland AG 2019 interse

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Hypersurface Singularities. Nearby and Vanishing Cycles,ycles are presented in Section 10.4 (to the computation of Euler characteristics of complex projective hypersurfaces), in Section 10.5 (for obtaining generalized Riemann–Hurwitz-type formulae), and in Section 10.6 (for deriving homological connectivity statements for the local topology of complex singularities).

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Brief Introduction to Sheaf Theory,In this chapter, we introduce the prerequisites needed later on (in Chapter .) for the sheaf-theoretic description of intersection homology groups.

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,Poincaré–Verdier Duality,In this chapter we introduce the dualizing functor and dualizing complex, and show how these can be used to deduce Poincaré and Alexander duality statements for manifolds.

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The Decomposition Package and Applications,This chapter is devoted to the “decomposition package”, consisting of Lefschetz-type results for perverse sheaves and intersection homology (Sections 9.1 and 9.2), as well as the BBDG decomposition theorem (Section 9.3). A sample of the numerous applications of the decomposition package is presented in Section 9.4.