Intersection Lawson homology

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Introduction to Lawson homology

Lawson homology has quite recently been proposed as an invariant for algebraic varieties. Various equivalent definitions have been suggested, each with its own merit. Here we discuss these for projective varieties and we also derive some basic properties for Lawson homology. For the general case we refer to Paulo Lima-Filho’s lectures in this volume.

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Chow Flag Variety and Lawson Homology

The Chow flag varieties are introduced and studied. In a family of pure dimensional projective complex varieties defined via Chow flag varieties, the isomorphism type of Lawson homology of a general member in the family is discussed. Applications to morphic cohomology and motivic cohomology on smooth projective complex varieties are discussed.

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Homology stratifications and intersection homology

A homology stratification is a filtered space with local homology groups constant on strata. Despite being used by Goresky and MacPherson [3] in their proof of topological invariance of intersection homology, homology stratifications do not appear to have been studied in any detail and their properties remain obscure. Here we use them to present a simplified version of the Goresky–MacPherson pr...

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Persistent Intersection Homology

The theory of intersection homology was developed to study the singularities of a topologically stratified space. This paper incorporates this theory into the already developed framework of persistent homology. We demonstrate that persistent intersection homology gives useful information about the relationship between an embedded stratified space and its singularities. We give, and prove the co...

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Intersection Homology II

In [19, 20] we introduced topological invariants IH~,(X) called intersection homology groups for the study of singular spaces X. These groups depend on the choice of a perversity p: a perversity is a function from {2, 3, ...} to the non-negative integers such that both /~(c) and c 2 / ~ ( c ) are positive and increasing functions of c (2.1). The group IHr is defined for spaces X called pseudoma...

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ژورنال

عنوان ژورنال: Transactions of the American Mathematical Society

سال: 1997

ISSN: 0002-9947,1088-6850

DOI: 10.1090/s0002-9947-97-01790-x