Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shifting chain maps in quandle homology and cocycle invariants   Quandle homology theory has been developed and cocycles have been used to
define invariants of oriented classical or surface links. We introduce a
shifting chain map $\sigma$ on each quandle chain complex that lowers the
dimensions by one. By using its pull-back $\sigma^\#$, each $2$-cocycle $\phi$
gives us the $3$-cocycle $\sigma^\# \phi$. For oriented classical links in the
$3$-space, we explore relation between their quandle $2$-cocycle invariants
associated with $\phi$ and their shadow $3$-cocycle invariants associated with
$\sigma^\# \phi$. For oriented surface links in the $4$-space, we explore how
powerful their quandle $3$-cocycle invariants associated with $\sigma^\# \phi$
are. Algebraic behavior of the shifting maps for low-dimensional (co)homology
groups is also discussed.

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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int