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A Spectral Sequence Concerning the Double Suspension.

Paul Selick (1981)

Inventiones mathematicae

Algebraic homotopy classes of rational functions

Christophe Cazanave (2012)

Annales scientifiques de l'École Normale Supérieure

Let $k$ be a field. We compute the set ${[𝐏^{1}, 𝐏^{1}]}^{N}$ ofnaivehomotopy classes of pointed $k$ -scheme endomorphisms of the projective line $𝐏^{1}$ . Our result compares well with Morel’s computation in [11] of thegroup ${[𝐏^{1}, 𝐏^{1}]}^{𝐀^{1}}$ of $𝐀^{1}$ -homotopy classes of pointed endomorphisms of $𝐏^{1}$ : the set ${[𝐏^{1}, 𝐏^{1}]}^{N}$ admits an a priori monoid structure such that the canonical map ${[𝐏^{1}, 𝐏^{1}]}^{N} \to {[𝐏^{1}, 𝐏^{1}]}^{𝐀^{1}}$ is a group completion.

Coincidence free pairs of maps

Ulrich Koschorke (2006)

Archivum Mathematicum

This paper centers around two basic problems of topological coincidence theory. First, try to measure (with the help of Nielsen and minimum numbers) how far a given pair of maps is from being loose, i.e. from being homotopic to a pair of coincidence free maps. Secondly, describe the set of loose pairs of homotopy classes. We give a brief (and necessarily very incomplete) survey of some old and new advances concerning the first problem. Then we attack the second problem mainly in the setting of homotopy...

Complex 2 Plane Bundles over CP(n).

Larry Smith (1978)

Manuscripta mathematica

Dehnungsuntersuchungen an Sphärenabbildungen.

Harald Hefter (1982)

Inventiones mathematicae

Detecting Stable Homotopy Classes by Primary BP Cohomology Operations.

Larry Smith, Raphael Zahler (1972)

Mathematische Zeitschrift

Freudenthal-Invariante.

Dietmar Arlt (1971)

Manuscripta mathematica

Geometric interpretations of the generalized Hopf invariant.

Ulrich Koschorke, Brian Sanderson (1977)

Mathematica Scandinavica

Geometry of normed bilinear maps and the 16-square problem.

K.Y. Lam, P.Y.H. Yiu (1989)

Mathematische Annalen

La décomposition des espaces des lacets et la torsion impaire des groupes d'homotopie

Dale Husemoller (1979/1980)

Séminaire Bourbaki

On link maps and their homotopy classification.

Ulrich Koschorke (1990)

Mathematische Annalen

On links with one codimension two compontent.

Peter Hilton, Roger Fenn (1992)

Forum mathematicum

Representation types and 2-primary homotopy groups of certain compact Lie groups.

Davis, Donald M. (2003)

Homology, Homotopy and Applications

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.

Currently displaying 1 – 20 of 20