Zobrazeno 1 - 10
of 27
pro vyhledávání: '"Broaddus, Nathan"'
Publikováno v:
Trans. Amer. Math. Soc. 376 (2023), 2557-2572
Let $M_n$ be the connect sum of $n$ copies of $S^2 \times S^1$. A classical theorem of Laudenbach says that the mapping class group $\text{Mod}(M_n)$ is an extension of $\text{Out}(F_n)$ by a group $(\mathbb{Z}/2)^n$ generated by sphere twists. We pr
Externí odkaz:
http://arxiv.org/abs/2012.01529
We give two proofs that appropriately defined congruence subgroups of the mapping class group of a surface with punctures/boundary have enormous amounts of rational cohomology in their virtual cohomological dimension. In particular we give bounds tha
Externí odkaz:
http://arxiv.org/abs/2003.10913
Aramayona and Leininger have provided a "finite rigid subset" $\mathfrak{X}(\Sigma)$ of the curve complex $\mathscr{C}(\Sigma)$ of a surface $\Sigma = \Sigma^n_g$, characterized by the fact that any simplicial injection $\mathfrak{X}(\Sigma) \to \mat
Externí odkaz:
http://arxiv.org/abs/1311.7646
Publikováno v:
Israel Journal of Mathematics; Apr2024, Vol. 260 Issue 1, p303-340, 38p
Akademický článek
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Autor:
Broaddus, Nathan
Publikováno v:
Duke Math. J. 161, no. 10 (2012), 1943-1969
By the work of Harer, the reduced homology of the complex of curves is a fundamental cohomological object associated to all torsion free finite index subgroups of the mapping class group. We call this homology group the Steinberg module of the mappin
Externí odkaz:
http://arxiv.org/abs/0711.0011
Johnson has defined a surjective homomorphism from the Torelli subgroup of the mapping class group of the surface of genus $g$ with one boundary component to $\wedge^3 H$, the third exterior product of the homology of the surface. Morita then extende
Externí odkaz:
http://arxiv.org/abs/0708.3861
Publikováno v:
C. R. Acad. Sci. Paris, Ser. I 345 (2007) 449--452
We bound the value of the Casson invariant of any integral homology 3-sphere $M$ by a constant times the distance-squared to the identity, measured in any word metric on the Torelli group $\T$, of the element of $\T$ associated to any Heegaard splitt
Externí odkaz:
http://arxiv.org/abs/0707.2264
Publikováno v:
Comment. Math. Helv. 86 (2011), 537-556
We prove that various subgroups of the mapping class group $Mod(\Sigma)$ of a surface $\Sigma$ are at least exponentially distorted. Examples include the Torelli group (answering a question of Hamenstadt), the "point-pushing" and surface braid subgro
Externí odkaz:
http://arxiv.org/abs/0707.2262
Autor:
Broaddus, Nathan
Hempel has shown that the fundamental groups of knot complements are residually finite. This implies that every nontrivial knot must have a finite-sheeted, noncyclic cover. We give an explicit bound, $\Phi (c)$, such that if $K$ is a nontrivial knot
Externí odkaz:
http://arxiv.org/abs/math/0401120