New techniques for computing geometric index

Kathryn B. Andrist (Avtor), Dennis Garity (Avtor), Dušan Repovš (Avtor), David Wright (Avtor)

Povzetek

We introduce new general techniques for computing the geometric index of a link ▫$L$▫ in the interior of a solid torus ▫$T$▫. These techniques simplify and unify previous ad hoc methods used to compute the geometric index in specific examples and allow a simple computation of geometric index for new examples where the index was not previously known. The geometric index measures the minimum number of times any meridional disc of ▫$T$▫ must intersect ▫$L$▫. It is related to the algebraic index in the sense that adding up signed intersections of an interior simple closed curve ▫$C$▫ in ▫$T$▫ with a meridional disc gives ▫$\pm$▫ the algebraic index of ▫$C$▫ in ▫$T$▫. One key idea is introducing the notion of geometric index for solid chambers of the form ▫$B^2 \times I$▫ in ▫$T$▫. We prove that if a solid torus can be divided into solid chambers by meridional discs in a specific (and often easy to obtain) way, then the geometric index can be easily computed.

Ključne besede

algebraic index;geometric index;Whitehead link;Bing link;McMillan link;Gabai link;Antoine link;

Podatki

Jezik:	Angleški jezik
Leto izida:	2017
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	UL FMF - Fakulteta za matematiko in fiziko
UDK:	515.124
COBISS:	18167129
ISSN:	1660-5446
Št. ogledov:	395
Št. prenosov:	296
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Vrsta dela (COBISS):	Članek v reviji
Strani:	art. 237 (15 str.)
Letnik:	ǂVol. ǂ14
Zvezek:	ǂiss. ǂ6
Čas izdaje:	2017
DOI:	10.1007/s00009-017-1036-1
ID:	11216345