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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Periodic Phenomena in homotopy theory
同伦理论 周期现象
2023/1/4
Chromatic homotopy theory uses the algebraic geometry of smooth 1-parameter formal groups to separate stable homotopy theory into periodic layers. The 1st layer recovers the image of Adams’ J homomorp...
Structured Stable Homotopy Theory and the Descent Problem for the Algebraic K-theory of Fields
Structured Stable Homotopy Theory Algebraic K-theory
2015/7/7
his is a relative result which asserts that the K-theory spectra of any two
algebraically closed fields of a given characteristic are equivalent to each other
after completion at a prime not e...
Towards a homotopy theory of higher dimensional transition systems
homotopy theory dimensional transition systems
2010/11/1
We proved in a previous work that Cattani-Sassone's higher dimensional transition systems can be interpreted as a small-orthogonality class of a topological locally finitely presentable category of w...
Relative categories: Another model for the homotopy theory of homotopy theories
model homotopy theory
2010/11/1
We lift Charles Rezk's complete Segal space model structure on the category of simplicial spaces to a Quillen equivalent one on the category of relative categories.
Category of fibrant objects is a convenient framework to do homotopy theory, introduced and developed by Ken Brown. In this paper, we apply it to the category of C^{*}-algebras. In particular, we get...
Bar-cobar duality for operads in stable homotopy theory
Bar-cobar duality stable homotopy theory
2010/9/1
We extend bar-cobar duality, defined for operads of chain complexes by Getzler and Jones, to operads of spectra in the sense of stable homotopy theory. Our main result is the existence
of a Quillen e...
The homotopy theory of function spaces: A survey
Function space monoid of self-equivalence free loop space
2010/9/1
We survey research on the homotopy theory of the space map(X, Y )consisting of all continuous functions between two topological spaces. We summarize progress on various classification problems for the...