Inscriere cercetatori

Premii Ad Astra

premii Ad Astra

Asociația Ad Astra a anunțat câștigătorii Premiilor Ad Astra 2022: Proiectul și-a propus identificarea și popularizarea modelelor de succes, a rezultatelor excepționale ale cercetătorilor români din țară și din afara ei.

Asociatia Ad Astra a cercetatorilor romani lanseaza BAZA DE DATE A CERCETATORILOR ROMANI DIN DIASPORA. Scopul acestei baze de date este aceea de a stimula colaborarea dintre cercetatorii romani de peste hotare dar si cu cercetatorii din Romania. Cercetatorii care doresc sa fie nominalizati in aceasta baza de date sunt rugati sa trimita un email la

Homotopy type invariants of four-dimensional knot complements

Domenii publicaţii > Matematica + Tipuri publicaţii > Tezã de doctorat (nepublicatã)

Autori: A.I. Suciu

Editorial: Columbia University, New York, NY, 1984.


This thesis studies the homotopy type of smooth four dimensional knot complements. In contrast with the classical case, high-dimensional knot complements with fundamental group different from are never aspherical. The second homotopy group already provides examples of the way in which a knot in S^4 can fail to be determined by its fundamental group (C. McA. Gordon, S. P. Plotnick).

A natural class of knots to investigate is ribbon knots. They bound immersed disks with „ribbon singularities”. A method is given for computing pi_2 of such knot complements. I show that there are infinitely many ribbon knots in S^4 with isomorphic pi_1 but distinct pi_2 (viewed as pi_1-modules). They appear as boundaries of distinct ribbon disk pairs with the same exterior. These knots have the fundamental group of the spun trefoil, but none in a spun knot.

To a four-dimensional knot complement, one can associate a certain cohomology class, the first k-invariant of Eilenberg, MacLane and Whitehead. In a joint paper, Plotnick and I showed that there are arbitrarily many knots in S^4 whose complements have isomorphic pi_1 and pi_2 (as pi_1 – modules), but distinct k-invariants. Here I prove this result using examples which are somewhat more natural and easier to produce. They are constructed from a fibered knot with fiber a punctured lens space and a ribbon knot by surgery.

The proofs involve writing down explicit cell complexes, computing twisted cohomology groups, combinatorial group theory and calculations in group rings.

Cuvinte cheie: Knots in the 4-sphere, homotopy type