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A famous result by Thom states that Oriented Bordism classes are determined by characteristic numbers; specifically, two closed manifolds are orientedly bordant if and only if they have the same ...

I need to find various ways of performing two surgeries on a collection of circles so that the resulting 2-dimensional cobordism (the trace of the surgeries) is connected. How can I find these ? up ...

In the paper "A splitting theorem for manifolds" by S.E. Cappell, https://www.maths.ed.ac.uk/~v1ranick/papers/capsplit.pdf the following "inverse" of the Seifert-van Kampen theorem for closed ...