Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New obstructions to doubly slicing knots   A knot in the 3-sphere is called doubly slice if it is a slice of an
unknotted 2-sphere in the 4-sphere. We give a bi-sequence of new obstructions
for a knot being doubly slice. We construct it following the idea of
Cochran-Orr-Teichner's filtration of the classical knot concordance group. This
yields a bi-filtration of the monoid of knots (under the connected sum
operation) indexed by pairs of half integers. Doubly slice knots lie in the
intersection of this bi-filtration. We construct examples of knots which
illustrate non-triviality of this bi-filtration at all levels. In particular,
these are new examples of algebraically doubly slice knots that are not doubly
slice, and many of these knots are slice. Cheeger-Gromov's von Neumann rho
invariants play a key role to show non-triviality of this bi-filtration. We
also show that some classical invariants are reflected at the initial levels of
this bi-filtration, and obtain a bi-filtration of the double concordance group.

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The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th