Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dirac operators, heat kernels and microlocal analysis Part II: analytic
  surgery   Let X be a closed Riemannian manifold and let H\hookrightarrow X be an
embedded hypersurface. Let X=X_+ \cup_H X_- be a decomposition of X into two
manifolds with boundary, with X_+ \cap X_- = H. In this expository article,
surgery -- or gluing -- formul\ae for several geometric and spectral invariants
associated to a Dirac-type operator \eth_X on X are presented. Considered in
detail are: the index of \eth_X, the index bundle and the determinant bundle
associated to a family of such operators, the eta invariant and the analytic
torsion. In each case the precise form of the surgery theorems, as well as the
different techniques used to prove them, are surveyed.

22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga