Configuration Spaces.

Подвижные полюсы мероморфных линейных систем на $\mathbb{P}^1(\mathbb{C})$ в комплексной плоскости

“…Из длинной точной последователь-ности гомотопических групп видим, что при всех k 2 имеет место π k ( Z) = π k (Z). В работе [6] было вычислено π k (Z) и показано, что для всех k 2…”

On Braid Groups, Free Groups, and the Loop Space of the 2-Sphere

“…The long exact homotopy sequence of the fundamental fibration sequence due to Fadell, and Neuwirth [14] can be regarded as determining the homotopy type of the loop space for the simplicial group obtained from the pure braid groups.…”

“…(1) Introduction (2) On the holomorph of a group, and the pure braid groups as group extensions (3) Quotients of the pure braid group, and the maps B n → Aut(K n ) (4) On link homotopy and related homotopy groups (5) On looping AP * (6) On embeddings of residually nilpotent groups (7) The simplicial structure for AP * (8) The Lie algebra associated to the descending central series for P n+1 (9) On Θ n : F n → P n+1 (10) On the proof of Theorem 9.1 (11) On Vassiliev invariants, the mod-p descending central series, and the BousfieldKan spectral sequence (12) On braid groups, and axioms for connected CW -complexes (13) Proof of Theorem 1.4 (14) Appendix: a sample computation…”

Spinning particles, braid groups and solitons

“…For example, it can be shown that B F 2 (IRIP 2 ) is not isomorphic to B F 2 (S 2 ). For any closed, nonorientable surface M (2) NO it has been shown that π 2 (Q n (M (2) NO )) = {e} (for IRIP 2 see [38], for all higher genuses see [4]). Thus, (2.2) becomes (compare to…”

“…However, until Section 8 we will restrict ourselves to those described above since many interesting features can already be seen at this level. For example, if the particles are structureless -that is, Y is just a point -then E = M and π 1 (Q E n (M )) is the n-string braid group B n (M ) of the manifold M [3] [4]. Given an IUR ρ of B n (M ), n ≥ 2, one can determine the statistics of the n identical particles in the corresponding quantum theory by restricting ρ to those elements of B n (M ) representing local permutations of the particles [5].…”