Manifold theoretic compactifications of configuration spaces

@misc{citeulike:311215, abstract = {We present new definitions for and give a comprehensive treatment of the canonical compactification of configuration spaces due to Fulton-MacPherson and Axelrod-Singer in the setting of smooth manifolds, as well as a simplicial variant of this compactification initiated by Kontsevich. Our constructions are elementary and give simple global coordinates for the compactified configuration space of a general manifold embedded in Euclidean space. We stratify the canonical compactification, identifying the diffeomorphism types of the strata in terms of spaces of configurations in the tangent bundle, and give completely explicit local coordinates around the strata as needed to define a manifold with corners. We analyze the quotient map from the canonical to the simplicial compactification, showing it is a homotopy equivalence. We define projection maps and diagonal maps, which for the simplicial variant satisfy cosimplicial identities.}, archivePrefix = {arXiv}, author = {Sinha, Dev}, citeulike-article-id = {311215}, eprint = {math.GT/0306385}, keywords = {category-theory, combinatorics, graphs, mathematics}, month = {Jul}, posted-at = {2005-09-04 06:33:51}, priority = {2}, title = {Manifold theoretic compactifications of configuration spaces}, url = {http://arxiv.org/abs/math.GT/0306385}, year = {2004} }

TY - ELEC ID - citeulike:311215 L3 - citeulike-article-id:311215 N2 - We present new definitions for and give a comprehensive treatment of the canonical compactification of configuration spaces due to Fulton-MacPherson and Axelrod-Singer in the setting of smooth manifolds, as well as a simplicial variant of this compactification initiated by Kontsevich. Our constructions are elementary and give simple global coordinates for the compactified configuration space of a general manifold embedded in Euclidean space. We stratify the canonical compactification, identifying the diffeomorphism types of the strata in terms of spaces of configurations in the tangent bundle, and give completely explicit local coordinates around the strata as needed to define a manifold with corners. We analyze the quotient map from the canonical to the simplicial compactification, showing it is a homotopy equivalence. We define projection maps and diagonal maps, which for the simplicial variant satisfy cosimplicial identities. TI - Manifold theoretic compactifications of configuration spaces KW - category-theory KW - combinatorics KW - graphs KW - mathematics AU - Sinha, Dev PY - 2004/Jul/06/ UR - http://arxiv.org/abs/math.GT/0306385 ER -