Publication

Distortion of Mappings and $L_{q,p}$-Cohomology

Marc Troyanov
2009
Journal Articles

Abstract

We study some relation between some geometrically defined classes of diffeomorphisms between manifolds and the $L_{q,p}$ -cohomology of these manifolds. Some applications to vanishing and non vanishing results in $L_{q,p}$ -cohomology are given.

Official source

https://infoscience.epfl.ch/entities/publication/687b1e68-4178-4cc2-b7f7-cf208eda6958

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Marc Troyanov
2009
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/687b1e68-4178-4cc2-b7f7-cf208eda6958

About this result

Related concepts (32)

Kodaira vanishing theorem

In mathematics, the Kodaira vanishing theorem is a basic result of complex manifold theory and complex algebraic geometry, describing general conditions under which sheaf cohomology groups with indices q > 0 are automatically zero. The implications for the group with index q = 0 is usually that its dimension — the number of independent global sections — coincides with a holomorphic Euler characteristic that can be computed using the Hirzebruch–Riemann–Roch theorem.

Cohomology

In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewed as a method of assigning richer algebraic invariants to a space than homology. Some versions of cohomology arise by dualizing the construction of homology. In other words, cochains are functions on the group of chains in homology theory.

Binary relation

In mathematics, a binary relation associates elements of one set, called the domain, with elements of another set, called the codomain. A binary relation over sets X and Y is a new set of ordered pairs (x, y) consisting of elements x in X and y in Y. It is a generalization of the more widely understood idea of a unary function. It encodes the common concept of relation: an element x is related to an element y, if and only if the pair (x, y) belongs to the set of ordered pairs that defines the binary relation.

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