arXiv subjects

Volker W. Thürey

Publications and source records attributed to Volker W. Thürey.

4 recordsLinked to original sources

arXiv2014

Homology Functors with Cubical Bars

This work arose from efforts to generalise the usual cubical boundary by using different 'weights' for opposite faces, but still to obtain a chain complex, and this method was found to generalise. We describe a variant of the classical singular homology theory, in which the usual boundary (n-1)-cubes of each n-cube are replaced by combinations of internal (n-1)-cubes parallel to the boundary. This defines a generalised homology theory, but the usual singular homology can be recovered by taking the quotient by the degenerate singular cubes.

math.KT↗

arXiv2013

The Complex Angle in Normed Spaces

We consider a generalized angle in complex normed vector spaces. Its definition corresponds to the definition of the well known Euclidean angle in real inner product spaces. Not surprisingly it yields complex values as `angles'. This `angle' has some simple properties, which are known from the usual angle in real inner product spaces. But to do ordinary Euclidean geometry real angles are necessary. We show that even in a complex normed space there are many pure real valued `angles'. The situation improves yet in inner product spaces. There we can use the known theory of orthogonal systems to find many pairs of vectors with real angles, and to do geometry which is based on the Greeks 2000 years ago.

math.FA↗

arXiv2012

Hölder Functionals and Quotients

We describe an inequality of finite or infinite sequences of real numbers and their quotients. More precisely, we compare the quotient of Hölder functionals of two sequences of numbers with the sum of their quotients. In the last section we investigate the `wideness' of the inequality, i.e. we show that both the inequality can converge into an equality, and the difference between the two sides of the inequality can be arbitrary large.

math.CA↗

arXiv2011

A Boundary Operator for Simplices

We generalize the very well known boundary operator of the ordinary singular homology theory, defined in many books about algebraic topology. We describe a variant of this ordinary simplicial boundary operator where the usual boundary (n-1)-simplices of each n-simplex are replaced by combinations of internal (n-1)- simplices parallel to the faces. This construction may lead to an infinite class of extraordinary non-isomorphic homology theories. We show further some interesting constructions on the standard simplex.

math.GT↗