Stable homotopy group, higher algebra and the telescope Conjecture
Stable homotopy group, higher algebra and the telescope Conjecture
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Tomer Schlank, Hebrew University of Jerusalem
A fundamental motivating problem in homotopy theory is the attempt to the study of stable homotopy groups of spheres.听The mathematical听object that binds听 stable homotopy groups together听is a spectrum.听听Spectra are the homotopy theorist abelian groups, they have a fundamental place in algebraic topology but also appear in arithmetic geometry, differential topology, mathematical physics and symplectic geometry. In a similar vein to the way that abelian groups are the bedrock of algebra and algebraic geometry we can take a similar approach of spectra.听 I will discuss the picture that emerges and how one can use it to learn听 about the stable homotopy groups of spheres.