loop spaces造句

例句与造句

1. There are more complicated operations on the Floer homology of a cotangent bundle that correspond to the string topology operations on the homology of the loop space of the underlying manifold.
2. Examples are the Fukaya category Fuk ( X ) and loop space ?X where X is a topological space and-algebras as A  "-categories with one object.
3. An important property of this functor is that it is a left adjoint to the functor \ Omega taking a ( based ) space X to its loop space \ Omega X.
4. We know the homology of the base and total space, so our intuition tells us that the Serre spectral sequence should be able to tell us the homology of the loop space.
5. Witten shortly after applied the Duistermaat Heckman formula to loop spaces and showed that this formally gave the Atiyah Singer index theorem for the Dirac operator; this idea was lectured on by Atiyah.
6. It's difficult to find loop spaces in a sentence. 用loop spaces造句挺难的
7. The importance of " A "  "-operads in homotopy theory stems from this relationship between algebras over " A "  "-operads and loop spaces.
8. The objects in the image have the structure of infinite loop spaces; whence, the notion is a generalization of the corresponding notion ( stabilization ( topology ) ) in classical algebraic topology.
9. where G / O denotes the homotopy fiber of the map J \ colon BO \ to BG, which is an infinite loop space and hence maps into it define a generalized cohomology theory.
10. Observe that the loop space \ Omega Y injects into the mapping fibre : \ Omega Y \ to Mf, as it consists of those maps that both start and end at the basepoint y _ 0.
11. He showed that these spaces possess alternative infinite loop space structures which are in fact better from the following point of view : Recall that there is a surgery obstruction map from normal invariants to the L-group.
12. In the last years, interest in the space of all free loops LX has grown with the advent of string topology, i . e . the study of new algebraic structures on the homology of the free loop space.
13. The " K "-groups of the exact category are the homotopy groups of & Omega; " BQC ", the loop space of the geometric realization ( taking the loop space corrects the indexing ).
14. The " K "-groups of the exact category are the homotopy groups of & Omega; " BQC ", the loop space of the geometric realization ( taking the loop space corrects the indexing ).
15. For Hamiltonians that are quadratic at infinity, the Floer homology is the singular homology of the free loop space of M ( proofs of various versions of this statement are due to Viterbo, Salamon Weber, Abbondandolo Schwarz, and Cohen ).
16. Define a topological space B ^ + C by B ^ + C = \ Omega B QC where \ Omega is a loop space functor and B QC is the classifying space of the category " QC " ( geometric realization of the nerve ).
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