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F r o m W i k i p e d i a , t h e f r e e e n c y c l o p e d i a
Education
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He did his graduate studies at Princeton University , obtaining his Ph.D. in 1970. His thesis, written under the supervision of Ralph Fox , was titled On homology spheres .
Research
[ edit ]
An early result of González-Acuña is that a group G is the homomorphic image of some knot group if and only if G is finitely generated and has weight at most one. This result (a "remarkable theorem", as Lee Neuwirth called it in his review),
was published in 1975 in Annals of Mathematics . In 1978, together with José María Montesinos, he answered a question posed by Fox, proving the existence of 2-knots whose groups have infinitely many ends .[citation needed ]
With Hamish Short , González-Acuña proposed and worked on the cabling conjecture : the only knots in the 3-sphere which admit a reducible Dehn surgery , i.e. a surgery which results in a reducible 3-manifold, are the cable knots .[citation needed ]
See also
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Selected publications
[ edit ]
González-Acuña, F., Homomorphs of knot groups , Annals of Mathematics (2 ) 102 (1975), no. 2, 37–377. MR 0379671
González-Acuña, F., Montesinos, José M., Ends of knot groups , Annals of Mathematics (2 ) 108 (1978), no. 1, 91–96. MR 0559794
González-Acuña, F., Short, Hamish, Knot surgery and primeness. Math. Proc. Cambridge Philos. Soc. 99 (1986), no. 1, 89–102. MR 0809502
J.C. Gómez-Larrañaga, F.J. González-Acuña, J. Hoste. Minimal Atlases on 3-manifolds , Math. Proc. Camb. Phil. Soc. 109 (1991), 105–115. MR 1075124
References
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External links
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R e t r i e v e d f r o m " https://en.wikipedia.org/w/index.php?title=Francisco_Javier_González-Acuña&oldid=1221331360 "
C a t e g o r i e s :
● L i v i n g p e o p l e
● 2 0 t h - c e n t u r y M e x i c a n m a t h e m a t i c i a n s
● 2 1 s t - c e n t u r y M e x i c a n m a t h e m a t i c i a n s
● P r i n c e t o n U n i v e r s i t y a l u m n i
● T o p o l o g i s t s
● A c a d e m i c s t a f f o f t h e N a t i o n a l A u t o n o m o u s U n i v e r s i t y o f M e x i c o
● M e x i c a n s c i e n t i s t s t u b s
● M a t h e m a t i c i a n s t u b s
H i d d e n c a t e g o r i e s :
● A r t i c l e s l a c k i n g i n - t e x t c i t a t i o n s f r o m J a n u a r y 2 0 2 3
● A l l a r t i c l e s l a c k i n g i n - t e x t c i t a t i o n s
● A l l a r t i c l e s w i t h u n s o u r c e d s t a t e m e n t s
● A r t i c l e s w i t h u n s o u r c e d s t a t e m e n t s f r o m J a n u a r y 2 0 2 3
● W e b a r c h i v e t e m p l a t e w a y b a c k l i n k s
● A r t i c l e s w i t h V I A F i d e n t i f i e r s
● A r t i c l e s w i t h J 9 U i d e n t i f i e r s
● A r t i c l e s w i t h L C C N i d e n t i f i e r s
● A r t i c l e s w i t h M A T H S N i d e n t i f i e r s
● A r t i c l e s w i t h M G P i d e n t i f i e r s
● Y e a r o f b i r t h m i s s i n g ( l i v i n g p e o p l e )
● A l l s t u b a r t i c l e s
● T h i s p a g e w a s l a s t e d i t e d o n 2 9 A p r i l 2 0 2 4 , a t 0 8 : 3 1 ( U T C ) .
● T e x t i s a v a i l a b l e u n d e r t h e C r e a t i v e C o m m o n s A t t r i b u t i o n - S h a r e A l i k e L i c e n s e 4 . 0 ;
a d d i t i o n a l t e r m s m a y a p p l y . B y u s i n g t h i s s i t e , y o u a g r e e t o t h e T e r m s o f U s e a n d P r i v a c y P o l i c y . W i k i p e d i a ® i s a r e g i s t e r e d t r a d e m a r k o f t h e W i k i m e d i a F o u n d a t i o n , I n c . , a n o n - p r o f i t o r g a n i z a t i o n .
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