Francisco Javier González-Acuña (nickname "Fico") is a mathematician in the

UNAM The National Autonomous University of Mexico (, UNAM) is a public research university in Mexico. It has several campuses in Mexico City, and many others in various locations across Mexico, as well as a presence in nine countries. It also has 34 ...

's institute of mathematics and CIMAT, specializing in

low-dimensional topology In mathematics, low-dimensional topology is the branch of topology that studies manifolds, or more generally topological spaces, of four or fewer dimensions. Representative topics are the theory of 3-manifolds and 4-manifolds, knot theory, ...

Education

He did his graduate studies at

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

, obtaining his Ph.D. in 1970. His thesis, written under the supervision of

Ralph Fox Ralph Hartzler Fox (March 24, 1913 – December 23, 1973) was an American mathematician. As a professor at Princeton University, he taught and advised many of the contributors to the ''Golden Age of differential topology'', and he played ...

, was titled ''On homology spheres''.

Research

An early result of González-Acuña is that a

group A group is a number of persons or things that are located, gathered, or classed together. Groups of people * Cultural group, a group whose members share the same cultural identity * Ethnic group, a group whose members share the same ethnic iden ...

''G'' is the homomorphic image of some

knot group In mathematics, a knot is an embedding of a circle into 3-dimensional Euclidean space. The knot group of a knot ''K'' is defined as the fundamental group of the knot complement of ''K'' in R3, :\pi_1(\mathbb^3 \setminus K). Other conventions consi ...

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 The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as t ...

''. 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. With Hamish Short, González-Acuña proposed and worked on the cabling conjecture: the only

knot A knot is an intentional complication in Rope, cordage which may be practical or decorative, or both. Practical knots are classified by function, including List of hitch knots, hitches, List of bend knots, bends, List of loop knots, loop knots, ...

s in the

3-sphere In mathematics, a hypersphere or 3-sphere is a 4-dimensional analogue of a sphere, and is the 3-dimensional n-sphere, ''n''-sphere. In 4-dimensional Euclidean space, it is the set of points equidistant from a fixed central point. The interior o ...

which admit a reducible

Dehn surgery In topology, a branch of mathematics, a Dehn surgery, named after Max Dehn, is a construction used to modify 3-manifolds. The process takes as input a 3-manifold together with a link. It is often conceptualized as two steps: ''drilling'' then '' ...

, i.e. a surgery which results in a reducible 3-manifold, are the cable knots.

Selected publications

* * * *

References

External links

portrait
*

Unsolvability of word problems with knot groups, at arXiv-2010 and L'Enseignement Mathematique. * https://www.cimat.mx/es/node/590 * https://escueladenudos.matem.unam.mx/ *https://www.smm.org.mx/noticia/121/escuela-fico-gonzalez-acuna-de-nudos-y-3-variedades Living people Year of birth missing (living people) 20th-century Mexican mathematicians 21st-century Mexican mathematicians Princeton University alumni Topologists Academic staff of the National Autonomous University of Mexico {{mathematician-stub

Education

Research

See also

Selected publications

References

External links