Algebraic Functions, Configuration Spaces, Teichmuller Spaces, and New Holomorphically Combinatorial Invariants

作者：Lin V Ya^*

来源：Functional Analysis and Its Applications, 2011, 45(3): 204-224.

DOI：10.1007/s10688-011-0024-7

• configuration spaces
• braid groups
• compositions of algebraic functions
• invariants of complex spaces

It is proved that, for n >= 4, the function u = u(n)(z), z = (z(1),..., zn). epsilon C(n), defined by the equation u(n) + z1u(n-1) + ... + z(n) = 0 cannot be a branch of an entire algebraic function g on C(n) that is a composition of entire algebraic functions depending on fewer than n-1 variables and has the same discriminant set as u(n). A key role is played by a description of holomorphic maps between configuration spaces of C and CP(1), which, in turn, involves Teichmuller spaces and new holomorphically combinatorial invariants of complex spaces.

• 出版日期2011-9