Rainer Vogt (1942–2015) was a mathematician who specialised in homotopy theory.
obituary at his former research group in Osnabrück.
Rainer Vogt, My time as Mike Boardman’s student and our work on infinite loop spaces (pdf)
He received his Ph.D. from the University of Warwick and his thesis advisor was Michael Boardman. He was a a full professor at Osnabrück University in Germany.
He coauthored with Boardman the famous book Homotopy invariant algebraic structures on topological spaces, Springer Lecture Notes in Math 347 (1973).
This book introduced the notion of weak Kan complex that was later popularized by André Joyal under the name quasi-category as a natural basis for the higher category theory of (∞,1)-categories.
An early application of the ideas from that book was in the proof of what is sometimes refereed to as Vogt’s theorem on categories of homotopy coherent maps, between homotopy coherent diagrams. This is briefly discussed at homotopy coherent diagram. It occurs in his paper
which gave a neat explicit construction/description of homotopy limits.
On convenient categories of topological spaces in the generality subsuming compactly generated topological spaces and Delta-generated topological spaces:
On a model structure on simplicial algebras for simplicial Lawvere theories:
On the iterated algebraic K-theory of (connective) ring spectra:
Some of the above material is taken from Joyal's CatLab – Rainer Vogt.
Last revised on October 1, 2021 at 00:55:08. See the history of this page for a list of all contributions to it.