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Simply connected right multipeak algebras and the separation property

Stanisław Kasjan (1999)

Colloquium Mathematicae

Let R=k(Q,I) be a finite-dimensional algebra over a field k determined by a bound quiver (Q,I). We show that if R is a simply connected right multipeak algebra which is chord-free and ˜ -free in the sense defined below then R has the separation property and there exists a preprojective component of the Auslander-Reiten quiver of the category prin(R) of prinjective R-modules. As a consequence we get in 4.6 a criterion for finite representation type of prin(R) in terms of the prinjective Tits quadratic...

Some examples of nonsingular Morse-Smale vector fields on S 3

F. Wesley Wilson Jr (1977)

Annales de l'institut Fourier

One wonders or not whether it is possible to determine the homotopy class of a vector field by examining some algebraic invariants associated with its qualitative behavior. In this paper, we investigate the algebraic invariants which are usually associated with the periodic solutions of non-singular Morse-Smale vector fields on the 3-sphere. We exhibit some examples for which there appears to be no correlation between the algebraic invariants of the periodic solutions and the homotopy classes of...

Some homotopy theoretical questions arising in Nielsen coincidence theory

Ulrich Koschorke (2009)

Banach Center Publications

Basic examples show that coincidence theory is intimately related to central subjects of differential topology and homotopy theory such as Kervaire invariants and divisibility properties of Whitehead products and of Hopf invariants. We recall some recent results and ask a few questions which seem to be important for a more comprehensive understanding.

Stable cohomotopy groups of compact spaces

Sławomir Nowak (2003)

Fundamenta Mathematicae

We show that one can reduce the study of global (in particular cohomological) properties of a compact Hausdorff space X to the study of its stable cohomotopy groups π s k ( X ) . Any cohomology functor on the homotopy category of compact spaces factorizes via the stable shape category ShStab. This is the main reason why the language and technique of stable shape theory can be used to describe and analyze the global structure of compact spaces. For a given Hausdorff compact space X, there exists a metric compact...

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