ON COBORDISM OF MANIFOLDS WITH CORNERS

By G. Laures. 2000

112 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5e855495546de5235b71e2b6994d5a38ff1b5180

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Citations in the corpus

The Mukai pairing, I: the Hochschild structure (2003, background): “ach to Hochschild homology via topology, which in a sense is orthogonal to the above one. In this approach we consider the 2-category C of 3-cobordisms with corners deﬁned as follows (for details see [22]): – objects of C are smooth, oriented 1-manifolds (i.e., disjoint unions of circles); – 1-morph”
A Steenrod square on Khovanov homology (2012, unknown): “†It is also a 〈k − 1〉-manifold in the sense of [6].”
Geometric cycles, index theory and twisted K-homology (2007, unknown): “13 There is a notion of cobordism of manifolds with boundary and corners, see [32] and [12].”
Quadratic functions in geometry, topology, and M-theory (2002, background): “For more information see [18, 26, 19] and for a discussion in connection with cobordism see [39].”
Algebraic topology and modular forms (2002, background): “There is a geometric interpretation of this filtration: a framed manifold M has filtration ≥ s if it occurs as a codimension n corner in a manifold N with corners, equipped with suitable almost complex structures on its faces (see [32]).”
On manifolds with corners (2009, methodology): “Laures [10] defines a cobordism theory for manifolds with corners, which has been applied in Topological Quantum Field Theory, by Lauda and Pfeiffer [9] for instance.”
A general Fredholm theory I: A splicing-based differential geometry (2006, background): “This concept is related to some notion occurring in [15].”
A note on the (∞,n)–category of cobordisms (2015, methodology): “ions Mpaq XpRmˆr0,1skpbqq “ Mpbq are transverse for all bă a. To prove that any k-bordism admits a neat embedding we use that any xky-manifold admits a compatible collaring: Lemma 8.8 (Lemma 2.1.6 in [Lau00]). For aP r1sk we write 1´a“ p1,...,1q´a. Any xky-manifold Madmits a xky-diagram Cof embeddin”