 
Summary: STATEMENT OF RESEARCH
MOHAMED AIT NOUH
Introduction: My field of study is knot theory. A knot (resp. link) k is a smooth embedding of
S1 (resp. a disjoint union of circles) in S3 = R3 {±} (e.g. the most basic knots are depicted in Fig. 1).
Unknot Trefoil
Figure eight knot
Figure 1:
I am interested in the interplay between knot theory and dimension four topology and geometry, via
twisting operations. To define a twisting operation, we need to define Dehn surgery.
Dehn surgery: (see Figure 2) Let N(k) be a tubular neighborhood of a knot k the S3. Then a
3manifold obtained by
p
q
Dehn surgery (
p
q
Q {±}) along k in S3 is the new 3manifold denoted
S3
(k,
p
