arXiv subjects

Nikita Golub

Publications and source records attributed to Nikita Golub.

4 recordsLinked to original sources

arXiv2026

Sheaves on Grothendieck constructions

In this paper we introduce a generalisation of a covariant Grothendieck construction to the setting of sites. We study the basic properties of defined site structures on Grothendieck constructions as well as we treat the cohomological aspects of corresponding toposes of sheaves. Despite the fact that the toposes of $G$-equivariant sheaves $Sh_G(X)$ have been introduced in literature, their cohomological aspects have not been treated properly in a desired fashion. So in the end of the paper we study some of the acyclic families, introduce new type of acyclic resolutions which we call the $G$-equivariant Godement resolutions, the degree of actions, and some other basic cohomological concepts arising in $Sh_G(X)$.

math.CT↗

arXiv2026

Algebraically and geometrically minimal DG-models of diagrams of spaces

We extend Sullivan's rational homotopy theory by constructing geometrically and algebraically minimal models for diagrams of simply connected spaces over a class of finite indexing categories. Both classes classify rational diagram homotopy types, but their minimality conditions can differ. We also show that, in contrast to classical rational homotopy theory, H-diagrams need not split into products of Eilenberg--MacLane diagrams, and characterize the indexing categories for which every H-diagram admits such a splitting. Also we apply this to computation of automorphism groups of rational homotopy types of certain diagrams of spaces.

math.AT↗

arXiv2026

On the Derivation of Twisted K-Theory from M-Theory

In a restricted untwisted sector, Diaconescu, Moore & Witten (2000, 2003) gave a quantum M-theoretic consistency check, at the level of partition functions, of what one may call "Hypothesis K", namely that magnetic and electric type IIA brane charges are jointly quantized in K-theory. We show that the more recently discussed "Hypothesis H" --- that magnetic and electric charges in 11D are jointly quantized in coHomotopy --- together with a topological smallness condition on the M-theory circle, systematically implies that IIA charges are quantized in a nonabelian deformation of twisted K-theory by the previously neglected non-linear NS1-brane charge. This is essentially a derivation of twisted K-theory from IR-completed 11D SuGra, and conversely a further consistency check on Hypothesis H from Hypothesis K. We motivate and precisely state this result, discuss its structural implications, and outline the elaborate algebro-topological proof.

hep-th↗

arXiv2025

Functorial languages in homological algebra and lower central series

There is a general phenomenon in algebra that numerous functors of homological significance admit characterization as derived limits of elementary functors defined over categories of free extensions. We demonstrate that upon restriction to appropriate subcategories of the category of groups, one may express analogously more interesting functors, including homology groups with cyclic coefficients. Moreover, we are laying the foundations of the so-called $\mathbf{fr}_\infty$-language, extending the $\mathbf{fr}$-language of Roman Mikhailov and Sergei O. Ivanov. This language is constructed by augmenting the $\mathbf{fr}$-language through the introduction of an infinite family of letters $\mathbf{fr}$ corresponding to the lower central series $γ_m(R)$ of the group of relations and leads to some neat computations.

math.KT↗