holomorphic automorphisms of universal cover of configuration spaces - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T09:59:07Z http://mathoverflow.net/feeds/question/120774 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/120774/holomorphic-automorphisms-of-universal-cover-of-configuration-spaces holomorphic automorphisms of universal cover of configuration spaces Aakumadula 2013-02-04T15:08:03Z 2013-02-06T12:03:05Z <p>Hello everyone,</p> <p>I have been trying (without success) to determine the following. Let $P$ denote the space of monic polynomials of degree $n$ with complex coefficients, which have distinct roots. It is known that the fundamental group of this space is the braid group $B_n$. Let $X \rightarrow P$ denote the universal cover. Then $B_n\subset Aut (X)$ where $Aut (X)$ is the group of holomorphic automorphisms of $X$. For $n\geq 4$, is it true that $Aut (X)=B_n$? I do not see any other automorphisms (but I am a novice in the area). </p> http://mathoverflow.net/questions/120774/holomorphic-automorphisms-of-universal-cover-of-configuration-spaces/120816#120816 Answer by Aakumadula for holomorphic automorphisms of universal cover of configuration spaces Aakumadula 2013-02-05T01:07:15Z 2013-02-05T01:07:15Z <p>Misha has answered my question completely. </p>