Comparison of cobordism theories

Relying on results of Hopkins-Morel, we show that, for $X$ a quasi-projective variety over a field of characteristic zero, the canonical map $\Omega_n(X)\to MGL_{2n,n}'(X)$ is an isomorphism. Here $\Omega_*(X)$ is the theory of algebraic cobordism defined by Levine-Morel, and $MGL_{*,*}'$ is the Borel-Moore homology version of the theory of algebraic cobordism defined via the algebraic Thom complex in the Morel-Voevodsky motivic stable homotopy category.Comment: 22 page

On a conjecture of Morel

In this note we prove that the $\mathbb{A}^1$-connected component sheaf $a_{Nis}(\pi_0^{\mathbb{A}^1}(\mathcal{X}))$ of an $H$-group $\mathcal{X}$ is $\mathbb{A}^1$-invariant

Louise C. Morel, The Louisville Women\u27s City Club, and municipal housekeeping in Louisville, 1917-1935.

Louise C. Morel was a leading social reformer in Louisville from 1917 through the early 1940s. Morel\u27s work is a primary example of the continuation of Progressive Era ideals into the decades after the traditional end of the Progressive Era. Because the areas in which she worked were those that had traditionally appealed to and benefited women and children, Morel became known as a municipal housekeeper. With the help of fellow members of the Louisville Women\u27s City Club, Morel conducted numerous surveys, organized conventions to educate the public, gave speeches, and urged city leaders to institute reforms in various areas. The issues in which Morel was interested include tuberculosis, garbage separation and disposal, housing quality, sewer expansion, and improvement of public buildings and outdoor areas. Morel\u27s work influenced women both in Louisville and across the state, and left a lasting imprint on the city