pith. machine review for the scientific record. sign in

arxiv: 2510.13764 · v2 · submitted 2025-10-15 · 🧮 math.GT · math.QA

Recognition: unknown

The minimal Rickard complexes of braids on two strands

Joshua Wang

Authors on Pith no claims yet
classification 🧮 math.GT math.QA
keywords complexbraidcoloredrickardstrandsclosurehomologyminimal
0
0 comments X
read the original abstract

The Rickard complex of a braid with strands colored by positive integers is a chain complex of singular Soergel bimodules. The complex determines the colored triply-graded homology and colored sl(N) homology of the braid closure, when closure is color-compatible. For each braid on two strands with any colors, we construct a minimal complex that is homotopy equivalent to its Rickard complex. It is not obtained by laborious simplification; instead, it is defined directly by explicit formulas obtained by educated guesswork and reverse engineering.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Link homology and loop homology

    math.GT 2026-04 unverdicted novelty 7.0

    The k-colored sl(N) homology of T(2,2m+1) stabilizes as m to infinity to the integral homology of the free loop space of Gr(k,N).