Results 1 
6 of
6
Selfcoincidences in higher codimensions
 J. Reine Angew. Math
"... Abstract. When can a map between manifolds be deformed away from itself? We describe a (normal bordism) obstruction which is often computable and in general much stronger than the classical primary obstruction in cohomology. In particular, it answers our question completely in a large dimension rang ..."
Abstract

Cited by 8 (6 self)
 Add to MetaCart
(Show Context)
Abstract. When can a map between manifolds be deformed away from itself? We describe a (normal bordism) obstruction which is often computable and in general much stronger than the classical primary obstruction in cohomology. In particular, it answers our question completely in a large dimension range. As an illustration we give explicit criteria in three sample settings: projections from Stiefel manifolds to Grassmannians, sphere bundle projections and maps defined on spheres. In the first example a theorem of Becker and Schultz concerning the framed bordism class of a compact Lie group plays a central role; our approach yields also a very short geometric proof (included as an appendix) of this result. I.
MTheory with Framed Corners and Tertiary Index Invariants
 SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS
, 2014
"... The study of the partition function in Mtheory involves the use of index theory on a twelvedimensional bounding manifold. In eleven dimensions, viewed as a boundary, this is given by secondary index invariants such as the Atiyah–Patodi–Singer etainvariant, the Chern–Simons invariant, or the Ada ..."
Abstract

Cited by 5 (4 self)
 Add to MetaCart
(Show Context)
The study of the partition function in Mtheory involves the use of index theory on a twelvedimensional bounding manifold. In eleven dimensions, viewed as a boundary, this is given by secondary index invariants such as the Atiyah–Patodi–Singer etainvariant, the Chern–Simons invariant, or the Adams einvariant. If the elevendimensional manifold itself has a boundary, the resulting tendimensional manifold can be viewed as a codimension two corner. The partition function in this context has been studied by the author in relation to index theory for manifolds with corners, essentially on the product of two intervals. In this paper, we focus on the case of framed manifolds (which are automatically Spin) and provide a formulation of the refined partition function using a tertiary index invariant, namely the finvariant introduced by Laures within elliptic cohomology. We describe the context globally, connecting the various spaces and theories around Mtheory, and providing a physical realization and interpretation of some ingredients appearing in the constructions due to Bunke–Naumann and Bodecker. The formulation leads to a natural interpretation of anomalies using corners and uncovers some resulting constraints in the heterotic corner. The analysis for type IIA leads to a physical identification of various components of etaforms appearing in the formula for the phase of the partition function.