Tootfinder

Colored knot Floer homology: structures and examples
Akram Alishahi, Eugene Gorsky, Beibei Liu
https://arxiv.org/abs/2508.21776 https://arxiv.org/pdf/2508.…

Colored knot Floer homology: structures and examples
Inspired by the $S^n$ colored version of Khovanov and Khovanov-Rozansky homology, we define a colored version of knot Floer homology by studying the colimit of a directed system of link Floer homology with infinite full twists. Specifically, our $n$-colored knot Floer homology of a knot $K$ is then defined as the colimit of the link Floer homology of $(n, mn)$-cables of $K$ by fixing $n$ and letting $m$ goes to infinity. We show that the colimit of the infinite full twists is a module over the …

Filter Quotient Model Structures
Nima Rasekh
https://arxiv.org/abs/2508.07735 https://arxiv.org/pdf/2508.07735

Filter Quotient Model Structures
The filter quotient construction is a particular instance of a filtered colimit of categories. It has primarily been considered in the context of categorical logic, where it has been used effectively to construct non-trivial models, for example new models of set theory. In this work we prove that given a model category and a suitable notion of filter of subterminal objects, the filter quotient construction will preserve the model structure. We also show that this new model structure inherits …

A Dwyer-Rezk classification for polynomial functors in Weiss calculus
David Barnes, Magdalena K\k{e}dziorek, Niall Taggart
https://arxiv.org/abs/2508.03808 https://

A Dwyer-Rezk classification for polynomial functors in Weiss calculus
In Goodwillie calculus, unpublished work of Dwyer and Rezk provides a classification of reduced filtered colimit preserving $d$-excisive functors from pointed spaces to spectra as spectrum-valued functors on the category of finite sets of cardinality at most $d$ and epimorphisms. We prove through different methods the analogous result in Weiss calculus: $d$-polynomial functors are equivalent to spectrum-valued functors on the category of finite-dimensional inner product spaces of dimension at m…

Semi-infinite parabolic IC-sheaf II: the Ran space version
Gurbir Dhillon, Sergey Lysenko
https://arxiv.org/abs/2508.01527 https://arxiv.org/pdf/2508.01527…

Semi-infinite parabolic IC-sheaf II: the Ran space version
This paper is a sequel to arXiv:2310.0638. Let G be a split reductive group. We define the parabolic semi-infinite category on the Ran version of the affine Grassmanian Gr_{G,Ran}. We study the semi-infinite parabolic IC-sheaf in this category. We provide several descriptions of this object, one as certain colimit, another as an intermediate extension in certain category. We relate the global and local semi-infinite categories of sheaves. We also relate the intersection cohomology sheaf of the …