Singular fibers of two-colored maps and cobordism invariants
نویسندگان
چکیده
منابع مشابه
Cobordism of singular maps
Throughout this paper we consider smooth maps of positive codimensions, having only stable singularities (see [Ar2], §1.4 in Chapter 1). We prove a conjecture due to M. Kazarian, connecting two classifying spaces in singularity theory for this type of singular maps.. These spaces are: 1) Kazarian’s space (generalising Vassiliev’s algebraic complex and) showing which cohomology classes are repre...
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Recently Galatius, Madsen, Tillmann and Weiss identified the homotopy type of the classifying space of the cobordism category of embedded d-dimensional manifolds [7] for each positive integer d. Their result lead to a new proof of the generalized standard Mumford conjecture. We extend the main theorem of [7] to the case of cobordism categories of embedded d-dimensional manifolds with prescribed...
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In [24] the first named author developed the theory of singular fibers of generic differentiable maps between manifolds of negative codimension. Here, the codimension of a map f W M !N between manifolds is defined to be k D dim N dim M . For k 0, the fiber over a point in N is a discrete set of points, as long as the map is generic enough, and we can study the topology of such maps by using the...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2008
ISSN: 0030-8730
DOI: 10.2140/pjm.2008.234.379