A Whitehead theorem for periodic homotopy groups

We show that $v_n$-periodic homotopy groups detect homotopy equivalences between simply-connected finite CW-complexes

Simplicial and Dendroidal Homotopy Theory

This open access book offers a self-contained introduction to the homotopy theory of simplicial and dendroidal sets and spaces. These are essential for the study of categories, operads, and algebraic structure up to coherent homotopy. The dendroidal theory combines the combinatorics of trees with the theory of Quillen model categories. Dendroidal sets are a natural generalization of simplicial sets from the point of view of operads. In this book, the simplicial approach to higher category theory is generalized to a dendroidal approach to higher operad theory. This dendroidal theory of higher operads is carefully developed in this book. The book also provides an original account of the more established simplicial approach to infinity-categories, which is developed in parallel to the dendroidal theory to emphasize the similarities and differences. Simplicial and Dendroidal Homotopy Theory is a complete introduction, carefully written with the beginning researcher in mind and ideally suited for seminars and courses. It can also be used as a standalone introduction to simplicial homotopy theory and to the theory of infinity-categories, or a standalone introduction to the theory of Quillen model categories and Bousfield localization

Partition complexes and trees

We construct a functor from the partition complex of a finite set A to a category of trees with leaves labelled by A and prove that it is homotopy initial. This construction and our proof are elementary and require very few preliminaries, but imply an equivalence between different bar constructions of an operad in great generality

Characterization of cytochrome P450 monooxygenase CYP154H1 from the thermophilic soil bacterium Thermobifida fusca

Cytochrome P450 monooxygenases are valuable biocatalysts due to their ability to hydroxylate unactivated carbon atoms using molecular oxygen. We have cloned the gene for a new cytochrome P450 monooxygenase, named CYP154H1, from the moderately thermophilic soil bacterium Thermobifida fusca. The enzyme was overexpressed in Escherichia coli at up to 14% of total soluble protein and purified to homogeneity in three steps. CYP154H1 activity was reconstituted using putidaredoxin reductase and putidaredoxin from Pseudomonas putida DSM 50198 as surrogate electron transfer partners. In biocatalytic reactions with different aliphatic and aromatic substrates of varying size, the enzyme converted small aromatic and arylaliphatic compounds like ethylbenzene, styrene, and indole. Furthermore, CYP154H1 also accepted different arylaliphatic sulfides as substrates chemoselectively forming the corresponding sulfoxides and sulfones. The enzyme is moderately thermostable with an apparent melting temperature of 67°C and exhibited still 90% of initial activity after incubation at 50°C

Lie algebras and vnv_n-periodic spaces

I will discuss an infinity-category obtained from that of pointed spaces by inverting the maps inducing isomorphisms in $v_n$-periodic homotopy groups. The case $n = 0$ corresponds to rational homotopy theory. In analogy with Quillenâ s results in the rational case, I will outline how this $v_n$-periodic homotopy theory is equivalent to the homotopy theory of Lie algebras in $T(n)$-local spectra (or a variant for $K(n)$-local spectra). One can also compare it to the homotopy theory of cocommutative coalgebras in $T(n)$-local spectra, where there is only an equivalence up to a certain "Goodwillie convergence" issue. I will describe the relevant operadic and cooperadic structures and a form of Koszul duality relevant to this setting.Non UBCUnreviewedAuthor affiliation: University of CopenhagenPostdoctora