2015/08/27 by Yasha Savelyev, Savelyev, Yasha, Egor Shelukhin +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #Equivalence (formal languages) #FOS: Mathematics #FOS: Physical sciences #Hamiltonian (control theory) #Hilbert space #Homotopy #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Mathematical Physics (math-ph) #Mathematics #Pure mathematics #Symplectic Geometry (math.SG) #math-ph #math.AT #math.DG #math.KT #math.MP #math.SG
paper · pdf · doi:10.48550/arxiv.1508.06793
22 pages; improvements in exposition, version accepted by JSG
openalex publication_date 2015/08/27 · arxiv created 2019/01/18 · arxiv updated 2019/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We introduce new invariants of Hamiltonian fibrations with values in the suitably twisted K-theory of the base. Inspired by techniques of geometric quantization, our invariants arise from the family analytic index of a family of natural Spinc-Dirac operators. As an application we give new examples of non-trivial Hamiltonian fibrations, that have not been previously detected by other methods. As one crucial ingredient we construct a potentially new homotopy equivalence map, with a certain naturality property, from BU to the space of index 0 Fredholm operators on a Hilbert space, using elements of modern theory of homotopy colimits.