Document Zbl 0929.57003

from until

One-Line Search

add line

Document Type:

Journal Articles

Collection Articles

Books

arXiv Preprints

Document Type:

Journal Articles

Collection Articles

Books

arXiv Preprints

Reset all

New Multi-Line Search

Help

Examples

Geometry Search for the term Geometry in any field. Queries are case-independent.

Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.

"Topological group" Phrases (multi-words) should be set in "straight quotation marks".

au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.

Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.

Quasi* map* py: 1989 The resulting documents have publication year 1989.

so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.

"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.

dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.

py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).

la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Fields

any	anywhere
an	internal document identifier
au	author, editor
ai	internal author identifier
ti	title
la	language
so	source
ab	review, abstract
py	publication year
rv	reviewer
cc	MSC code
ut	uncontrolled term
dt	document type (j: journal article; b: book; a: book article)

Operators

a & b	logic and
a \| b	logic or
!ab	logic not
abc*	right wildcard
"ab c"	phrase
(ab c)	parentheses

The tunnel number of the sum of \(n\) knots is at least \(n\). (English) Zbl 0929.57003

Topology 38, No. 2, 265-270 (1999).

The tunnel number of a knot \(K\) in \(S^3\) is the minimum number of disjoint proper tunnels needed to be drilled into the complement of a tubular neighborhood of \(K\) in order to obtain a handlebody. It has been known for some time now that if a knot has tunnel number \(1\) then it is prime. This result is here generalized to show that if the tunnel number of \(K\) is \(n\) then \(K\) can be expressed as a connected sum of \(\leq n\) prime knots.

Reviewer: J.Levine (Waltham)

Cited in 2 Reviews

Cited in 21 Documents

MSC:

57M25

Knots and links in the \(3\)-sphere (MSC2010)

Keywords:

Heegaard decomposition

Cite Review PDF

Full Text: DOI arXiv