arXiv subjects

Djordje Baralic

Publications and source records attributed to Djordje Baralic.

21 records · Page 2Linked to original sources

arXiv2013

On Non-zero Degree Maps between Quasitoric 4-Manifolds

We study the map degrees between quasitoric 4-manifolds. Our results rely on Theorems proved by Duan and Wang. We determine the set D (M, N) of all possible map degrees from M to N when M and N are certain quasitoric 4-manifolds. The obtained sets of integers are interesting, e. g. those representable as the sum of two squares D (C P^2#C P^2, C P^2) or the sum of three squares D (C P^2 # C P^2 # C P^2, C P^2). Beside the general results about the map degrees between quasitoric 4-manifolds, the connections among Duan-Wang's approach, the quadratic forms, the number theory and the lattices is established.

math.GT↗

arXiv2012

Illumination of Pascal's Hexagrammum and Octagrammum Mysticum

We prove general results which include classical facts about 60 Pascal's lines as special cases. Along similar lines we establish analogous results about configurations of 2520 conics arising from Mystic Octagon. We offer a more combinatorial outlook on these results and their dual statements. Bezout's theorem is the main tool, however its application is guided by the empirical evidence and computer experiments with program Cinderella. We also emphasize a connection with $k$-nets of algebraic curves.

math.AG↗

arXiv2010

Topological obstructions to totally skew embeddings

Following Ghomi and Tabachnikov we study topological obstructions to totally skew embeddings of a smooth manifold M in Euclidean spaces. This problem is naturally related to the question of estimating the geometric dimension of the stable normal bundle of the configuration space F_2(M) of ordered pairs of distinct points in M. We demonstrate that in a number of interesting cases the lower bounds obtained by this method are quite accurate and very close to the best known general upper bound. We also provide some evidence for the conjecture that each n-dimensional, compact smooth manifold M^n (n>1), admits a totally skew embedding in the Euclidean space of dimension N = 4n-2alpha(n)+1 where alpha(n)=number of non-zero digits in the binary representation of n. This is a revised version of the paper (accepted for publication in A.M.S. Transactions).

math.AT↗