Seminar of the session "Algebraic topology, geometric and combinatorial group theory"
timetable:
Wed 25 Feb, 9:30 - 10:30, Aula Dini
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seminar: On the extended Vassiliev conjecture - Seminar of the session "Algebraic topology, geometric and combinatorial group theory" (2015)
speaker: Pavle V. M. Blagojević (Free University Berlin / Mathematical Institute SASA Belgrade)abstract: We present new upper bounds for the height of elements in the cohomology of the unordered configuration space \(H^*(\mathrm{Conf}_n(\mathbb{R}^d)/\mathfrak{S}_n;\mathbb{F}_p)\) with coefficients in the field \(\mathbb{F}_p\).
In the special case when \(d\) is a power of \(2\) and \(p=2\) we settle the original Vassiliev conjecture by proving that \(\mathrm{height}(H^*(\mathrm{Conf}_n(\mathbb{R}^d)/\mathfrak{S}_n;\mathbb{F}_2))=d\).
As applications of these results we obtain new lower bounds for the existence of complex \(k\)-regular maps as well as for complex \(\ell\)-skew maps \(\mathbb{C}^d\rightarrow\mathbb{C}^N\).
This is joint work with F. Cohen, W. Lück, G. M. Ziegler.
timetable:
Wed 25 Feb, 9:30 - 10:30, Aula Dini
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