The Chess conjecture

Sadykov, Rustam

doi:10.2140/agt.2003.3.777

Cited by 4 publications

(2 citation statements)

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“…Let δ be 0 if f is a fold map, and let δ be 1 otherwise. If the Morin map f : M n → Q n−k is not a cusp map and both M and Q are orientable, then perturb f to get a cusp map, see [Sad03], and denote this cusp map by f as well for simplicity.…”

Section: Computing the Characteristic Classes Of The Source Manifoldmentioning

confidence: 99%

“…− There exist fold maps and cusp maps of M into an almost parallelizable manifold only if the Euler characteristic χ(M ) is even, under the assumption that n−k is big enough [SS98]. Refinements of [SS98] include results for Morin maps as well when k is odd [An07,Sad03] but nothing is known when χ(M ) is even. − For odd k , the self-intersection class of the singular set of a generic corank 1 map…”

Section: Introductionmentioning

confidence: 99%

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Characteristic classes and existence of singular maps

Kalmar¹,

Terpai²

2012

Trans. Amer. Math. Soc.

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Abstract. The existence of a corank one map of negative codimension puts strong restrictions on the topology of the source manifold. It implies many vanishing theorems on characteristic classes and often even vanishing of the cobordism class of the source manifold. Most of our results lie deeper than just vanishing of Thom polynomials of the higher singularities. We blow up the singular map along the singular set and then perturb the arising nongeneric corank one map.

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Section: Computing the Characteristic Classes Of The Source Manifoldmentioning

confidence: 99%