{ "id": "1212.3547", "version": "v3", "published": "2012-12-14T17:59:58.000Z", "updated": "2014-04-17T08:09:11.000Z", "title": "Harer stability and orbifold cohomology", "authors": [ "Nicola Pagani" ], "comment": "10 pages. Corrected the attribution of the isomorphisms in equation (2)", "journal": "Pacific J. Math. 267 (2014), no.2, 465-477", "doi": "10.2140/pjm.2014..101", "categories": [ "math.AG", "math.AT" ], "abstract": "In this paper we review the combinatorics of the twisted sectors of $\\mathcal{M}_{g,n}$, and we exhibit a formula for the age of each of them in terms of the combinatorial data. Then we show that orbifold cohomology of $\\mathcal{M}_{g,n}$ when $g \\to \\infty$ reduces to its ordinary cohomology. We do this by showing that the twisted sector with minimal age is always the hyperelliptic twisted sector with all markings in the Weierstrass points; the age of the latter moduli space is just half its codimension in $\\mathcal{M}_{g,n}$.", "revisions": [ { "version": "v3", "updated": "2014-04-17T08:09:11.000Z" } ], "analyses": { "subjects": [ "14H10", "32G15", "55N32", "14N35", "14D23", "14H37", "55P50" ], "keywords": [ "orbifold cohomology", "harer stability", "combinatorial data", "ordinary cohomology", "minimal age" ], "tags": [ "journal article" ], "note": { "typesetting": "TeX", "pages": 10, "language": "en", "license": "arXiv", "status": "editable", "adsabs": "2012arXiv1212.3547P" } } }