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(beware that there is also Huzihiro Araki) Introducing what came to be known as the Dyer-Lashof operations: Discussion of -equivariant stable homotopy groups/equivariant stable cohomotopy of spheres: On real oriented cohomology theory in general and in particular on Real cobordism cohomology and Real K-theory: Shôrô Araki, -Cohomology Theories, Japanese Journal of Mathematics 4 2 (1978) 363-416 […

Huzihiro Araki, Relative Entropy of States of von Neumann Algebras, Publications of the Research Institute for Mathematical Sciences, 11 3 (1976) 809-833 (pdf, doi:10.2977/prims/1195191148)

under construction symmetric monoidal (∞,1)-category of spectra Special and general types group cohomology, nonabelian group cohomology, Lie group cohomology cohomology with constant coefficients / with a local system of coefficients Special notions Variants differential cohomology Extra structure Operations Theorems In algebraic topology, power operations are cohomology operations in multiplicat…

William Browder (1934-2025) Early discussion of what came to be known as Dyer-Lashof operations: On homology of H-spaces and their Pontryagin product: William Browder, Homology and Homotopy of H-Spaces, Proceedings of the National Academy of Sciences of the United States of America 46 4 (1960) 543-545 [jstor:70867] William Browder, p. 36 of: Torsion in H-Spaces, Annals of Mathematics, Second Seri…

symmetric monoidal (∞,1)-category of spectra An -algebra is an ∞-algebra over the E-k operad. -algebras are often called A-∞ algebras. See also algebra in an (∞,1)-category. An algebra in the symmetric monoidal (∞,1)-category Spec of spectra is a ring spectrum. The homology of an -algebra in chain complexes is a Gerstenhaber algebra. See E-∞ algebra. The homology of an -algebra for is a Poisson n…

An -fold iterated loop space canonically carries the structure of an -algebra (an algebra over the little n-disk operad ) with -equivariant structure maps Passing to ordinary homology of the loop space with coefficients in a finite field, , the Dyer-Lashof operations are essentially the pushforward/images in homology under the binary operation or rather, this map precomposed with Now, is equivale…

Introducing what came to be known as the Dyer-Lashof operations:

On -algebras in relation to the Dickey bracket of conserved currents in local field theory:

On -algebras in relation to the Dickey bracket of conserved currents in local field theory: On local BRST cohomology and BV-formalism: Glenn Barnich, Friedemann Brandt, Marc Henneaux, Local BRST cohomology in the antifield formalism: I. General theorems, Commun. Math. Phys. 174 (1995) 57-92 [arXiv:hep-th/9405109, doi:10.1007/BF02099464] Glenn Barnich, Marc Henneaux, Isomorphisms between the Batal…

interview by Kathryn Hess: video John McCleary: An appreciation of the work of Jim Stasheff (pdf) On -spaces and A-∞ algebras: Jim Stasheff, Homotopy associativity of H-spaces I, Trans. Amer. Math. Soc. 108 2 (1963) 275-292 [doi:10.2307/1993608] Jim Stasheff, Homotopy associativity of H-spaces II 108 2 (1963) 293-312 [doi:10.2307/1993609, doi:10.1090/S0002-9947-1963-0158400-5] On the simplicial d…

Tyler Lawson, Niko Naumann, Strictly commutative realizations of diagrams over the Steenrod algebra and topological modular forms at the prime 2, Int. Math. Res. Not. (2013) (arXiv:1203.1696)

Thomas J. Lada On homology of iterated loop spaces and the Dyer-Lashof operations?: On -algebras: Tom Lada, Jim Stasheff: Introduction to sh Lie algebras for physicists, Int. J. Theo. Phys. 32 (1993) 1087–1103 [doi:10.1007/BF00671791, arXiv:hep-th/9209099] Tom Lada, Martin Markl: Strongly homotopy Lie algebras, Communications in Algebra 23 6 (1995) [doi:10.1080/00927879508825335, arXiv:hep-th/940…

The homology of (iterated) based loop spaces (ordinary homology or generalized homology) carries special structure, reflecting the ∞-group-structure of based loop spaces. In particular, under mild technical conditions (see Milnor-Moore 65, p. 262, Halperin 92) the Pontrjagin ring-structure induced by concatenation of loops enhances the homology coalgebra induced by the diagonal maps to that of a …

beware that there is also Ralph Cohen. Frederick Ronald Cohen (1945-2022) On configuration spaces of points: On the real cohomology of (the Fulton-MacPherson compactification of) configuration spaces of ordered points in Euclidean space: Fred Cohen, Cohomology of braid spaces, Bull. Amer. Math. Soc. Volume 79, Number 4 (1973) 763-766 (euclid:1183534761) Fred Cohen: The homology of -Spaces, , In: …

J. Peter May is a homotopy theorist at the University of Chicago, inventor of operads as a technique for studying infinite loop spaces and spectra. Peter May’s work makes extensive use of enriched- and model-category theory as power tools in algebraic topology/homotopy theory, notably in discussion of highly structured spectra in MMSS00‘s Model categories of diagram spectra (for exposition see In…

On the maximal compact subalgebras of E9 and E10, respectively, and their finite-dimensional linear representations: Relating the E10 U-duality covariant sigma-model description of, hypothetically, M-theory to D=3 gauged supergravity: On tensor hierarchies in gauged supergravity: On relation of Borcherds algebras to tensor hierarchies in gauged supergravity: Jakob Palmkvist, Tensor hierarchies, B…

A connective spectrum is a connective object in the stable -category of spectra, hence a spectrum whose homotopy groups in all negative degrees are trivial: . These are equivalently: Connective spectra form a sub-(∞,1)-category of spectra There are objects in Spectra, though, that do not come from “naively” delooping a topological space infinitely many times. These are the non-connective spectra.…

nLab congruence subgroup Contents Definition Of the modular group Let n ∈ ℕ n \in \mathbb{N} be a natural number . Write p n : SL 2 ( ℤ ) → SL 2 ( ℤ / n ℤ ) p_n \;\colon\; SL_2(\mathbb{Z}) \to SL_2(\mathbb{Z}/n\mathbb{Z}) for the projection from the Moebius special linear group SL ( 2 , ℤ SL(2,\mathbb{Z} induced by the quotient projection ℤ → ℤ / n ℤ \mathbb{Z} \to \mathbb{Z}/n\mathbb{Z} to the i…

physics, mathematical physics, philosophy of physics theory (physics), model (physics) experiment, measurement, computable physics Axiomatizations Tools Structural phenomena Types of quantum field thories examples In the standard model of particle physics, the Yukawa couplings encode the interaction between the fundamental fermion fields and the Higgs field, and thus, via the Higgs mechanism, the…

Formally: Completing a PhD on the biophysical chemistry of nucleotides via molecular dynamics. Informally: A big fan of types, categories, and abstraction. Bad at algebra, but unwilling to quit trying. Having a grand time studying novel foundations of modern physics.