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1
P M Akhmetiev ,
On a new
integral formula for an invariant of $3$–component oriented
links , J. Geom. Phys. 53 (2005) 180 MR2110831
2
P Akhmetiev , A
Ruzmaikin , A fourth-order
topological invariant of magnetic or vortex lines , J.
Geom. Phys. 15 (1995) 95 MR1310943
3
V I Arnold ,
B A Khesin , Topological methods in
hydrodynamics , Applied Mathematical Sciences 125, Springer
(1998) MR1612569
4
D Auckly , L
Kapitanski , Analysis of
$S^2$–valued maps and Faddeev's model , Comm. Math.
Phys. 256 (2005) 611 MR2161273
5
M A Berger ,
Third-order link
integrals , J. Phys. A 23 (1990) 2787 MR1062985
6
M A Berger ,
Third-order braid
invariants , J. Physics A 24 (1991) 4027 MR1126646
7
H v. Bodecker , G
Hornig , Link
invariants of electromagnetic fields , Phys. Rev. Lett.
92 (2004) 030406 MR2068408
8
P Cromwell , E
Beltrami , M Rampichini , The Borromean rings ,
Math. Intelligencer 20 (1998) 53 MR1601839
9
D DeTurck , H
Gluck , R Komendarczyk , P Melvin , C
Shonkwiler , D S Vela-Vick , Triple linking
numbers, ambiguous Hopf invariants and integral formulas for
three-component links , Mat. Contemp. 34 (2008) 251
MR2588614
10
D DeTurck , H
Gluck , R Komendarczyk , P Melvin , C
Shonkwiler , D S Vela-Vick , Generalized Gauss maps
and integrals for three-component links: Toward higher
helicities for magnetic fields and fluid flows , J.
Math. Phys. 54 (2013) 013515
11
N W Evans ,
M A Berger , A hierarchy of linking
integrals , from: "Topological aspects of the dynamics of
fluids and plasmas" (editors H K Moffatt, G M
Zaslavsky, P Comte, M Tabor), NATO Adv. Sci. Inst. Ser. E Appl.
Sci. 218, Kluwer Acad. Publ. (1992) 237 MR1232234
12
C F Gauss ,
Integral formula for linking number , from: "Werke
Ergänzungsreihe, Band V" (editor C A F Peters), Georg
Olms Verlag (1975) 605
13
E Guadagnini , M
Martellini , M Mintchev , Wilson lines
in Chern–Simons theory and link invariants , Nuclear
Phys. B 330 (1990) 575 MR1043394
14
H Hopf , Über die Abbildungen der
dreidimensionalen Sphäre auf die Kugelfläche , Math.
Ann. 104 (1931) 637 MR1512691
15
G Hornig , C
Mayer , Towards a
third-order topological invariant for magnetic fields ,
J. Phys. A 35 (2002) 3945 MR1910658
16
B A Khesin ,
Geometry
of higher helicities , Mosc. Math. J. 3 (2003) 989
MR2078570
17
R Komendarczyk ,
The
third order helicity of magnetic fields via link maps ,
Comm. Math. Phys. 292 (2009) 431 MR2544738
18
R Komendarczyk ,
The third
order helicity of magnetic fields via link maps, II , J.
Math. Phys. 51 (2010) 122702 MR2779587
19
P Laurence , E
Stredulinsky , Asymptotic Massey
products, induced currents and Borromean torus links ,
J. Math. Phys. 41 (2000) 3170 MR1755498
20
L Leal , Link invariants
from classical Chern–Simons theory , Phys. Rev. D 66
(2002) 125007 MR1959509
21
L Leal , J
Pineda , The topological
theory of the Milnor invariant $\overline\mu(1,2,3)$ ,
Modern Phys. Lett. A 23 (2008) 205 MR2392325
22
W S Massey ,
Some higher order cohomology operations , from:
"Symposium internacional de topología algebraica" (editor
N C Flores), Universidad Nacional Autónoma de México
(1958) 145 MR0098366
23
W S Massey ,
Higher order linking numbers , from: "Conf. on Algebraic
Topology", Univ. of Illinois at Chicago Circle (1969) 174
MR0254832
24
J Milnor , Link groups , Ann.
of Math. 59 (1954) 177 MR0071020
25
H K Moffatt ,
The
degree of knottedness of tangled vortex lines , J. Fluid
Mech. 35 (1969) 117
26
M I Monastyrsky ,
V S Retakh , Topology of
linked defects in condensed matter , Comm. Math. Phys.
103 (1986) 445 MR832921
27
L Pontrjagin ,
A classification
of mappings of the three-dimensional complex into the
two-dimensional sphere , Rec. Math. [Mat. Sbornik] N. S.
9 (51) (1941) 331 MR0004780
28
T Rivière ,
High-dimensional helicities and rigidity of linked
foliations , Asian J. Math. 6 (2002) 505 MR1946345
29
A Ruzmaikin , P
Akhmetiev , Topological invariants of
magnetic fields, and the effect of reconnections , Phys.
Plasmas 1 (1994) 331 MR1269751
30
J H C
Whitehead , An expression of
Hopf's invariant as an integral , Proc. Nat. Acad. Sci.
USA 33 (1947) 117 MR0020255
31
L Woltjer , A theorem on
force-free magnetic fields , Proc. Nat. Acad. Sci. USA
44 (1958) 489 MR0096542