This book contains recent papers by participants in the Rokhlin Topology Seminar, organized by V. A. Rokhlin in the 1960s, when he moved to Leningrad. Since then, the seminar has continued to be one of the main centers of research in topology in Russia. The topics presented here are concerned with, or are motivated by, topology of specific geometric objects, from classical knots to complex projective surfaces and configurations of subspaces in real projective spaces.

A. I. Degtyarev -- Cohomology approach to killing structures

A. I. Degtyarev -- Classification of quartics having a nonsimple singular point. II

A. I. Degtyarev, S. Finashin, and G. Mikhalkin -- Generalized Pin-structures and some applications to low dimensional topology

J. Drobotukhina -- Classification of links in ${mathbb R}!P^3$ with at most six crossings

A. L. Felshtyn -- Reidemeister and Nielsen zeta functions, and Reidemeister torsion in the theory of dynamical systems

S. Finashin -- Variation of the Rokhlin function in higher dimensions

D. Fomin -- Stiefel orientations. I: Existence and constructions

M. Gusarov -- A new form of the Conway-Jones polynomial of oriented links

M. Gusarov -- On $n$-equivalence of knots and invariants of finite degree

I. V. Itenberg -- Rigid isotopy classification of curves of degree $6$ with one nondegenerate double point

V. F. Mazurovskii -- Configurations of at most six $(2n-1)$-dimensional subspaces of ${mathbb R}!P^{(4n-1)}$

G. Mikhalkin -- Congruences for real algebraic curves on an ellipsoid

N. Netsvetaev -- Diffeomorphism criteria for simply connected even-dimensional manifolds

V. M. Nezhinskii -- Homotopy theory for the classification of singular links

O. Viro -- Complex orientations of real algebraic surfaces

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