Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Witten Deformation and Its Application toward Morse Inequalities   In this undergraduate thesis, we present an analytical proof of the Morse
inequalities for closed smooth $n$-manifolds following Witten's approach. Using
techniques from PDE theory, the proof is reduced to study the eigenspaces and
eigenvalues of harmonic oscillators on $\mathbb{R}^n$.

22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat