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Topology of cell complexes and manifolds, classification of manifolds (e.g. smoothing, surgery), low dimensional topology (e.g. knot theory, invariants of 4-manifolds), embedding theory, combinatorial and PL topology, geometric group theory, infinite dimensional topology (e.g. Hilbert cube manifolds, theory of retracts).

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Circle-valued Morse function and minimal genus

I think the following two statements are true, and most likely are in the literature. If so, could someone point me to some references? If not, counterexamples? Let $Y$ be a closed oriented connected …
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