Triple Massey Products with weights in Galois cohomology
Eliyahu Matzri

TL;DR
This paper investigates the properties of triple Massey products in Galois cohomology, proving they contain zero under certain conditions and analyzing their structure using cohomological tools and algebraic theorems.
Contribution
It establishes new results on the vanishing of specific triple Massey products in Galois cohomology for arbitrary primes and explores their structure via symbols and algebraic methods.
Findings
Any defined 3MP of weight (n,1,m) with symbol entries contains zero.
For p=2, any defined 3MP of weight (1,k,1) with a symbol middle entry contains zero.
Uses algebraic tools to analyze the kernel of multiplication by a symbol in Galois cohomology.
Abstract
Fix an arbitrary prime . Let be a field containing a primitive -th root of unity, with absolute Galois group , and let denote its mod cohomology group . The triple Massey product of weight is a partially defined, multi-valued function %(in the mod- Galois cohomology) In this work we prove that for an arbitrary prime , any defined of weight , where the first and third entries are assumed to be symbols, contains zero; and that for any defined of the weight , where the middle entry is a symbol, contains zero. Finally, we use the description of the kernel of multiplication by a symbol to study general 3MP where the middle slot is a symbol. The main tools we will be using is Lemma 4.1…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Algebraic Geometry and Number Theory
