%0 Generic %1 gonzalezprieto2018topological %A González-Prieto, Ángel %D 2018 %K GIT %T Topological Geometric Invariant Theory and character varieties %U http://arxiv.org/abs/1807.08540 %X In this paper, we study a weaker version of algebraic quotient for the action of an algebraic group on an algebraic variety that is well behaved under stratification. Focusing on the topological properties of these quotients, we obtain a series of results about their structure and uniqueness. As an application, we compute the $K$-theory image of the Hodge structure of $SL_2(C)$-character varieties for free groups and surface groups, as well as their counterparts with punctures of Jordan type.

@misc{gonzalezprieto2018topological, abstract = {In this paper, we study a weaker version of algebraic quotient for the action of an algebraic group on an algebraic variety that is well behaved under stratification. Focusing on the topological properties of these quotients, we obtain a series of results about their structure and uniqueness. As an application, we compute the $K$-theory image of the Hodge structure of $\mathrm{SL}_2(\mathbb{C})$-character varieties for free groups and surface groups, as well as their counterparts with punctures of Jordan type.}, added-at = {2020-09-05T09:18:33.000+0200}, author = {González-Prieto, Ángel}, biburl = {https://www.bibsonomy.org/bibtex/25af73dbcf3d7e0f5f0d5919767d67037/simonechiarello}, description = {Topological Geometric Invariant Theory and character varieties}, interhash = {a01a511bee0e9d866dc2de82ad85cd47}, intrahash = {5af73dbcf3d7e0f5f0d5919767d67037}, keywords = {GIT}, note = {cite arxiv:1807.08540Comment: 38 pages. Major modifications in Section 4. Title changed}, timestamp = {2020-09-05T09:18:33.000+0200}, title = {Topological Geometric Invariant Theory and character varieties}, url = {http://arxiv.org/abs/1807.08540}, year = 2018 }