Combinatorics of orbit configuration spaces

[1804.06863] Combinatorics of orbit configuration spaces Skip to main content Search Submit Donate Log in Mathematics > Combinatorics arXiv:1804.06863 (math) [Submitted on 18 Apr 2018 ( v1 ), last revised 2 Oct 2020 (this version, v3)] Title: Combinatorics of orbit configuration spaces Authors: Christin Bibby , Nir Gadish View PDF HTML (experimental) Abstract: From a group action on a space, define a variant of the configuration space by insisting that no two points inhabit the same orbit. When the action is almost free, this "orbit configuration space" is the complement of an arrangement of subvarieties inside the cartesian product, and we use this structure to study its topology. We give an abstract combinatorial description of its poset of layers (connected components of intersections from the arrangement) which turns out to be of much independent interest as a generalization of partition and Dowling lattices. The close relationship to these classical posets is then exploited to give explicit cohomological calculations. Comments: 34 pages Subjects: Combinatorics (math.CO) ; Algebraic Topology (math.AT) Cite as: arXiv:1804.06863 [math.CO] (or arXiv:1804.06863v3 [math.CO] for this version) https://doi.org/10.48550/arXiv.1804.06863 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Int. Math. Res. Not. IMRN 2022:9 (2022), 6903-6947 Related DOI : https://doi.org/10.1093/imrn/rnaa296 Focus to learn more DOI(s) linking to related resources Submission history From: Christin Bibby [ view email ] [v1] Wed, 18 Apr 2018 18:16:55 UTC (34 KB) [v2] Thu, 30 Jan 2020 15:07:34 UTC (34 KB) [v3] Fri, 2 Oct 2020 17:55:12 UTC (36 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.CO < prev | next > new | recent | 2018-04 Change to browse by: math math.AT References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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