Research output: Working paper › Preprint
Research output: Working paper › Preprint
}
TY - UNPB
T1 - Steenrod operations via higher Bruhat orders
AU - Laplante-Anfossi, Guillaume
AU - Williams, Nicholas J.
N1 - 29 pages, 3 figures
PY - 2023/9/28
Y1 - 2023/9/28
N2 - The purpose of this paper is to establish a correspondence between the higher Bruhat orders of Yu. I. Manin and V. Schechtman, and the cup-$i$ coproducts defining Steenrod squares in cohomology. To any element of the higher Bruhat orders we associate a coproduct, recovering Steenrod's original ones from extremal elements in these orders. This correspondence allows us to interpret the coproducts geometrically in terms of zonotopal tilings, understand all possible choices of coproducts, and give conceptual proofs of their properties.
AB - The purpose of this paper is to establish a correspondence between the higher Bruhat orders of Yu. I. Manin and V. Schechtman, and the cup-$i$ coproducts defining Steenrod squares in cohomology. To any element of the higher Bruhat orders we associate a coproduct, recovering Steenrod's original ones from extremal elements in these orders. This correspondence allows us to interpret the coproducts geometrically in terms of zonotopal tilings, understand all possible choices of coproducts, and give conceptual proofs of their properties.
KW - math.AT
KW - math.CO
KW - 55U15, 55S10, 52C22, 52B11, 55S05
M3 - Preprint
BT - Steenrod operations via higher Bruhat orders
ER -