Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiplicative structures on cones and duality   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 describe the multiplicative structure on Rabinowitz Floer homology via cones
and we reprove the Poincar\'e duality theorem from this perspective. We
generalize the splitting theorem previously proved in the context of cotangent
bundles to large classes of Weinstein domains. We express the mixed cap
products in string topology in terms of loop products and coproducts, and we
describe extended loop homology entirely in terms of Morse homology. The paper
contains three appendices. The first one discusses multilinear shifts in a
multilinear setting. The second one, of operadic flavor, discusses sign
conventions and the language of trees to describe algebraic operations in a dg
setting. The third one contains a description of the product on extended loop
homology in the language of Morse theory and cones.

14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin