15,191 reputation
23059
bio website nd.edu/~lnicolae
location University of Notre Dame
age 49
visits member for 2 years, 10 months
seen 9 hours ago
I do mostly geometry and topology, with an analytic bias. For the past few years Morse theory has popped up in my research, but not in a conventional way.

15h
comment A fredholm index associated with two vector fields generating a 2 dimensional foliation
If $\dim M>2$ this is not a Fredholm operator.
1d
revised Notion of manifold curvature?
added 1 character in body
1d
answered Notion of manifold curvature?
Nov
16
revised What does analyticity imply in complex analysis?
added 1 character in body
Nov
16
answered What does analyticity imply in complex analysis?
Nov
14
comment Gompf's invariant of $2$-plane fields
Have you looked at Kronheimer and Mrowka's book Monopoles and 3-Manifolds?
Nov
13
awarded  Enlightened
Nov
12
awarded  Nice Answer
Nov
11
comment The difference between a handle decomposition and a CW decomposition
Let us continue this discussion in chat.
Nov
11
comment The difference between a handle decomposition and a CW decomposition
Also read the two paragraphs immediately following the statement of Theorem 3.5, page 13 of his paper front.math.ucdavis.edu/1012.3643
Nov
11
comment The difference between a handle decomposition and a CW decomposition
He refers to these assumptions as local triviality. Read the first paragraph in section 3, top page 10 of his paper front.math.ucdavis.edu/1012.3643
Nov
11
comment The difference between a handle decomposition and a CW decomposition
He assumes that near a critical point the metric is flat and the function $f$ has the form $f(x)=\pm x_1^2\pm x_2^2\pm \cdots \pm x_n^2$.
Nov
11
revised Exploiting the Linearity of the Pullback
added 1 character in body
Nov
10
comment Harmonic Crystal using Random Walk
Can you define $\langle\varphi(0)\rangle$?
Nov
10
awarded  Pundit
Nov
9
answered Exploiting the Linearity of the Pullback
Nov
9
awarded  Custodian
Nov
9
reviewed Reviewed Exploiting the Linearity of the Pullback
Nov
9
comment Exploiting the Linearity of the Pullback
From what I see, the functional map is the pullback by the inverse of $T$.
Nov
8
revised What are the “correct” conventions for defining Clifford algebras?
deleted 5 characters in body