Cacti and filtered distributive laws
Citation:
V.Dotsenko and J.Griffin, Cacti and filtered distributive laws, Algebraic and Geometric Topology, 14, 6, 2015, 3185-3225Download Item:
Abstract:
Motivated by the second author’s construction of a classifying space for the group of
pure symmetric automorphisms of a free product, we introduce and study a family of
topological operads, the operads of based cacti, defined for every pointed simplicial
set
.
Y
;
p
/
. These operads also admit linear versions, which are defined for every
augmented graded cocommutative coalgebra
C
. We show that the homology of the
topological operad of based
Y
–cacti is the linear operad of based
H
.
Y
/
–cacti. In
addition, we show that for every coalgebra
C
the operad of based
C
–cacti is Koszul.
To prove the latter result, we use the criterion of Koszulness for operads due to the
first author, utilising the notion of a filtered distributive law between two quadratic
operads. We also present a new proof of that criterion, which works over a ground
field of arbitrary characteristic
Author's Homepage:
http://people.tcd.ie/dotsenkvDescription:
PUBLISHED
Author: Dotsenko, Vladimir
Type of material:
Journal ArticleSeries/Report no:
Algebraic and Geometric Topology14
6
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cactiMetadata
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