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... zero section. For the bundle $L_{n}$ we see that there is a well-defined transverse section $[z_0, z_1] \mapsto [z_0, z_1, z_0^n - z_1^n]$ with precisely $n$ p

* $\Sigma(f)-P$ is an open manifold consisting of self-transverse double points of $f$. ...f:D^3\to\Rr^5$ over a general position map $g:S^2\to\Rr^4$ having only two transverse self-intersection points, where the smooth cone is defined by $f(tx):=(g(x)

$f_x(X)$ is transverse to a certain hyperplane $H\subset\CP^N$.

A generic immersion $\phi: S^q \to M$ has only double points with transverse crossings. Then $\mu([\phi]) \in {\Bbb Z}_2$ is defined to be the number

A flat bundle has a foliation by fibres and it also has a foliation transverse to the fibers, whose leaves are $$L_f:= ...$M$ is taut if for every leaf $\lambda$ of $\mathcal{F}$ there is a circle transverse to $\mathcal{F}$ which intersects $\lambda$.

...fold $N$ to $\Cc P^{n+1}$. The map $g$ has the pleasant feature that it is transverse to $\Cc P^n\subset \Cc P^{n+1}$ and the restriction of $g$ to a degree one ...^n)$, represent it by homotopy equivalence $f\colon M\to \Cc P^n$ which is transverse to $\Cc P^i\subset \Cc P^n$. The restriction of $f$ to a map $g\colon f^{-1

...or smooth). After Poincaré one studies the '''intersection number''' of ''transverse'' submanifolds or chains in $N$. ...n $x\in C_k(N;\Zz)$ and an $(n-k)$-chain $y\in C_{n-k}(N;\Zz)$ which are ''transverse'' to each other. The signed count of the intersections between $x$ and $y$

transverse to $U$: if $x\in T_U'$ and $L$ is the leaf of $\mathcal{F}$ passing through

...manifold $X$ with normal bundle $\nu_{Y \subset X}$ and that that $f$ is [[transverse]] to $Y$.

...,w')$ is described as follows. Choose representavives with $g_0$ and $g_1$ transverse. For every double point $(x_0,x_1)$ with $g_0(x_0)=g_1(x_1)=d$ determine th ...\widetilde{f_0})$ and $(f_1,\widetilde{f_1})$ choose $f_0$ and $f_1$ to be transverse. For every doublepoint $(x_0,x_1)$ with $f_0(x_0)=f_1(x_1)=d$ there exists

... \partial_1(W+(\phi^q))$, such that $\phi^{q+1}(S^q\times\{0\})$ meets the transverse sphere of the handle $(\phi^q)$ transversally in exactly one point. Conclud ...\phi^q_{i_0})$ transversally in exactly one point and is disjoint from the transverse spheres of the handles $(\phi^q_i)$ for $i\neq i_0$. Show that there is $\g

...athbb{Z}) \times C_{m-k}(\widetilde{M};\mathbb{Z}) \to \mathbb{Z}$$ counts transverse intersections between chains algebraically.

A flat bundle has a foliation by fibres and it also has a foliation transverse to the fibers, whose leaves are $$L_f:= ...$M$ is taut if for every leaf $\lambda$ of $\mathcal{F}$ there is a circle transverse to $\mathcal{F}$ which intersects $\lambda$.

A double point $x=(x_1,x_2)\in S_2(f_1,f_2)$ of $f_1$ and $f_2$ is ''transverse'' if the linear map ...erse intersection'') if $S_2(f_1,f_2)$ is finite and every double point is transverse.

...ooparrowright M^{n_1+n_2}$, $f_2:N_2^{n_2} \looparrowright M^{n_1+n_2}$ be transverse [[Π-trivial_map|$\pi$-trivial immersions]] of oriented manifolds with pres ...ht\widetilde{M}$, $\widetilde{f}_2:N_2\looparrowright\widetilde{M}$ have a transverse double point $$\widetilde{x} = (x_1,x_2) \in S_2(g(x)\widetilde{f}_1,\widet