Example of a pair of non-cobordant manifolds

You can just consider some simple bordism variants.

If you're considering oriented bordism, then the first example appears when considering bordisms between $4$-manifolds. The signature $\sigma(X^{4k})$ of an oriented $4k$-manifold $X^{4k}$ is an oriented bordism invariant. Now $$\sigma(S^4) = 0$$ and $$\sigma(\Bbb C P^2) = 1,$$ so $S^4$ and $\Bbb C P^2$ are not oriented bordant. In fact, $\Omega_4^{\mathrm{SO}} \cong \Bbb Z$ with generator $[\Bbb C P^2]$.

Proof that a finite separable extension has only finite many intermediate fields

Cauchy-Schwarz inequality for bilinear forms valued in an abstract vector space

Eclipse Editor: How to change file format from Dos to Unix

$\mathbb A^n(k)$ and $\mathbb A^n(k)\setminus \{0\}$ are not homeomorphic

Generalizing Ramanujan's sum of cubes identity?

Is there a math field that studies something like this?

$f(x)=x$ if $x$ irrational and $f(x)=p\sin\frac1q$ if $x$ rational

If $17! = 355687\underline{ab}8096000$. Then value of $(a,b)$ is

understanding git fetch then merge

Finding indefinite integral $\int{ \mathrm dx\over \sqrt{\sin^3 x+\sin (x+\alpha)}}$

Is $(V_1\otimes\cdots\otimes V_k)^\ast \simeq V_1^\ast\otimes \cdots \otimes V_k^\ast$ true for infinite dimensional spaces?

Does this statement about Hilbert spaces make any sense?