REVIEW 4 cited by
Multiplicative structures on cones and duality
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Multiplicative structures on cones and duality
read the original abstract
We initiate the study of multiplicative structures on cones and show that cones of Floer continuation maps fit naturally in this framework. We apply this to give a new description of the multiplicative structure on Rabinowitz Floer homology and cohomology, and to give a new proof of the Poincar\'e duality theorem which relates the two. The underlying algebraic structure admits two incarnations, both new, which we study and compare: on the one hand the structure of $A_2^+$-algebra on the space $\mathcal{A}$ of Floer chains, and on the other hand the structure of $A_2$-algebra involving $\mathcal{A}$, its dual $\mathcal{A}^\vee$ and a continuation map from $\mathcal{A}^\vee$ to $\mathcal{A}$.
Forward citations
Cited by 4 Pith papers
-
Generation of immersed Lagrangians by cocores
Exact Lagrangian immersions carrying positive-action bounding cochains - equivalently augmentations of their Legendrian lifts' Chekanov-Eliashberg algebras - are generated by the Lagrangian cocores of the ambient Wein...
-
Proper modules over Ginzburg dg algebras and compact Fukaya categories of plumbings
Compact Fukaya categories of general plumbings are generated by proper modules over associated Ginzburg dg algebras and equivalent to proper modules over wrapped Fukaya categories and to microlocal sheaves.
-
Reduced symplectic homology and string topology
Reduced loop homology is introduced so the loop product and coproduct form a unital infinitesimal anti-symmetric bialgebra satisfying a modified Sullivan relation, established via reduced symplectic homology on Weinst...
-
Generation of immersed Lagrangians by cocores
Exact Lagrangian immersions with augmentations or bounding cochains are generated by Lagrangian cocores in Weinstein manifolds.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.