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Abstract
We compute the bordism groups of fold maps with restricted multiplicities of regular points and no multiple fold points.
Abstract
We give a Pontryagin-Thom type construction for Stein factorizations of fold maps of 3-manifolds into the plane. As an application, we compute the cobordism group of Stein factorizations of fold maps of oriented 3-manifolds into the plane and the oriented cobordism group of fold maps of 3-manifolds into the plane. It turns out that these two groups are isomorphic to Z 2 ⊕ Z 2. We have the analogous results about bordism groups as well.
We prove that for n ≧ 1 and q > 0 the (oriented) cobordism group of fold maps of (oriented) ( n + q )-dimensional manifolds into ℝ n contains the direct sum of ⌊ q + 1)/2⌋ copies of the ( n − 1)th stable homotopy group of spheres as a direct summand. We also prove that for k ≧ 1 and q = 2 k −1 the cobordism group of fold maps of unoriented ( n + q )-dimensional manifolds into ℝ n also contains the n th stable homotopy group of the space ℝ P ∞ as a direct summand. We have the analogous results about bordism groups of fold maps as well.
Abstract
We prove new results about the vector field problem on the real flag manifolds O(n)/O(1) x O(1) x O(n - 2). For some infinite families of these manifolds, we completely solve the vector field problem.
Tobias Schönberg in 2015. The pole of this great circle represents the axis of the fold. Map varieties of this study ( Figs 19–22 and 24 ) were based primarily on the 1:50.000 scale geologic map of the region, published by Budai et al. (1999
