The space of immersed surfaces in a manifold

2012/03/15 by Oscar Randal-Williams, Oscar Randal‐Williams · 1 citation
Mathematics · #Cohomology #Combinatorics #Computer science #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Infinity #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Pure mathematics #Space (punctuation) #Topology (electrical circuits) #Torsion (gastropod) #math.AT #msc:55P47 #msc:57R15 #msc:58D10 #msc:58D29

paper · pdf · doi:10.1017/s0305004112000679

published as Mathematical Proceedings of the Cambridge Philosophical Society, 154 (3) (2013) 419-438 · 19 pages, 1 figure

arxiv created 2012/03/15 · openalex publication_date 2013/01/16 · arxiv updated 2013/04/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Abstract We study the cohomology of the space of immersed genus g surfaces in a simply-connected manifold. We compute the rational cohomology of this space in a stable range which goes to infinity with g . In fact, in this stable range we are also able to obtain information about torsion in the cohomology of this space, as long as we localise away from ( g -1).

Citations

• Towards an Enumerative Geometry of the Moduli Space of Curves
• Stable cohomology of the mapping class group with symplectic coefficients and of the universal Abel-Jacobi map
• The Classification of Immersions of Spheres in Euclidean Spaces
• Complex Analytic Coordinates in Almost Complex Manifolds

Cited by

• Mapping class groups and function spaces: a survey