Chromatic homotopy theory is algebraic when p > n2 + n + 1
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DOI: 10.1016/j.aim.2021.107958
Abstract: Abstract We show that if E is a p-local Landweber exact homology theory of height n and p > n 2 + n + 1 , then there exists an equivalence h S p E… read more here.
Keywords: chromatic homotopy; homotopy; theory; theory algebraic ... See more keywords
Monochromatic homotopy theory is asymptotically algebraic
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DOI: 10.1016/j.aim.2021.107999
Abstract: In previous work, we used an ∞-categorical version of ultraproducts to show that, for a fixed height n, the symmetric monoidal ∞-categories of En,p-local spectra are asymptotically algebraic in the prime p. In this paper,… read more here.
Keywords: homotopy theory; theory; asymptotically algebraic; monoidal categories ... See more keywords
The homotopy theory of complete modules
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DOI: 10.1016/j.jalgebra.2021.11.030
Abstract: Given a commutative ring $R$ and finitely generated ideal $I$, one can consider the classes of $I$-adically complete, $L_0^I$-complete and derived $I$-complete complexes. Under a mild assumption on the ideal $I$ called weak pro-regularity, these… read more here.
Keywords: homotopy theory; theory complete; complete complexes; complete modules ... See more keywords
Simple homotopy theory and nerve theorem for categories
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DOI: 10.1016/j.topol.2021.107609
Abstract: Abstract We study a combinatorial homotopy theory for small categories without a loop (loopfree categories) which is closely related to Whitehead's simple homotopy theory for regular CW-complexes with triangular cells. Quillen's theorem A and the… read more here.
Keywords: nerve theorem; simple homotopy; homotopy; homotopy theory ... See more keywords
MULTIPLICATIVE PARAMETRIZED HOMOTOPY THEORY VIA SYMMETRIC SPECTRA IN RETRACTIVE SPACES
Sign Up to like & getrecommendations! Published in 2020 at "Forum of Mathematics, Sigma"
DOI: 10.1017/fms.2020.11
Abstract: In order to treat multiplicative phenomena in twisted (co)homology, we introduce a new point-set-level framework for parametrized homotopy theory. We provide a convolution smash product that descends to the corresponding $\infty$-categorical product and allows for… read more here.
Keywords: parametrized homotopy; multiplicative parametrized; homotopy theory; theory via ... See more keywords
Homotopy theory of complete Lie algebras and Lie models of simplicial sets
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DOI: 10.1112/topo.12073
Abstract: In a previous work, by extending the classical Quillen construction to the non-simply connected case, we have built a pair of adjoint functors, 'model' and 'realization', between the categories of simplicial sets and complete differential… read more here.
Keywords: homotopy theory; lie algebras; simplicial sets; algebras lie ... See more keywords
Topological resolutions in K(2)‐local homotopy theory at the prime 2
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DOI: 10.1112/topo.12076
Abstract: We provide a topological duality resolution for the spectrum $E_2^{h\mathbb{S}_2^1}$, which itself can be used to build the $K(2)$-local sphere. The resolution is built from spectra of the form $E_2^{hF}$ where $E_2$ is the Morava… read more here.
Keywords: resolution; homotopy theory; resolutions local; topological resolutions ... See more keywords
The extended rational homotopy theory of operads
Sign Up to like & getrecommendations! Published in 2018 at "Georgian Mathematical Journal"
DOI: 10.1515/gmj-2018-0061
Abstract: Abstract In this paper, we set up a rational homotopy theory for operads in simplicial sets whose term of arity one is not necessarily reduced to an operadic unit, extending results obtained by the author… read more here.
Keywords: homotopy theory; rational homotopy; homotopy; theory operads ... See more keywords